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Volume `[bar(AB)bar(AC)bar(AD)]=|{:(2,3,-2),(6,-4,-8),(0,2,-5):}|`=138Transcript

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00:00 - 00:59 | latest given problem if we have been provided 3 lines L1 L2 and L3 such that I'll one line is having some direction ratios and it is passing through a point whose coordinates are also known to US and L2 visa line whose direction ratios are also been mentioned at the point is also existing online and do as another line l 3 is there which is having certain direction ratio and this line is intersecting line L1 and L2 at two distinct points that is C and now we have to festival evaluate the coordinates of a point c and the ant and after finding the coordinates of point cnd we have to find the volume of the parallelepiped that is formed by the vector a vector AC and vector a d the first of all overall we have to calculate the coordinates of point c and d right superstar fall at us understand and analyse the situation that if this is a line L1 this is a line l 2 |

01:00 - 01:59 | 10000 line L3 right so what comes next is this is L1 and this is our point see what is intersecting point of line L1 and L2 and this is a line l to and this is my point which is intersecting point offline L2 and L3 light we have not been provided with the coordinates of points easily can assume the coordinates of point ciaz x333 and coordinates of point he can be used as expo-av 484 now we need to evaluate the coordinates of the point c and d so that we can find the volume of the parallel by which is formed by these three types of all we need to learn about the general principle to form equation of a line when the direction ratios are given for the line so we know that the equation of a line is been given by the formula x minus x not divided by a = 2y - why not divided by an equal to Z - That not divide |

02:00 - 02:59 | and that is equal to a constant letters in Lambda right now this is basically equation of a line in which the line is passing through the point x x not come away not come yet not this become the equation of a line now in our case we have been provided with the direction ratios for line L1 L2 L3 respectively and also the coordinates of point A and B which are lying on the line L1 and L2 can easily find the equation of line and well as well which would be x minus now we have the coordinates of point as7262 right and the direction reach you for line L1 are - 32 Oz latest write it out here -32 cover for now we can easily find the equation for line as ones that are to be equal to x minus 7 / -3 that should be equal to Y - 6 / to that should be equal to Z - 4 this is actually that - |

03:00 - 03:59 | right side -2 divided by 4 and that should be equal to a constant London in our case right now we can use the same principle to find the equation of a line and now we know that I'll to is a line which is passing through the point B and the coordinates of point P R 5343 we can write it down here the coordinates of point veer534 and direction ratios for Reliance 2213 so we can write here that took a 13 right now what are we going to do we can write the equation for L2 by using the same principles of this would be at minus 5 by 2 = 2y - 3 by 1 equals to Z - 4 by 3 right now this time we have assume the cost and that is Lambda to write so when we have these two equations we can easily calculate the coordinates of points which is lying on I and K and a line l 2 |

04:00 - 04:59 | light so if we have considered a line L1 then for that line we can see that the value for as could be equal to 7 - of thrill and the one the value for Y equal to 6 plus 2 Lander one and value for that would be equal to 2 + 4 London right now similarly we can also find the values for xy as that is the coordinates of any point which is lying on a line l to by using this equation so we can say that would be equal to 5 + 2 Lander 27 leave I would be equal to 3 + Lambda to and that would be equal to 4 plus 3 lehenga to write so now we have to formulate the equation of line health research that we can find the coordinates of point c and pointy now we are going to use the same principle this principle to find the equation for 93 tired so we know that L3 and we know that |

05:00 - 05:59 | the equation for line LC would be something like x minus 3 / the direction ratio for light and 3 are known to us that are to -2 and -1 se latest write down here to -2 and -1 so this would be x minus 3 by 2 = 2y - 3 Y - 2 = 2 - z3 by -1 and this constant is this type = 2 Lander 3 right now we can again write the values for the point that is the coordinates of the point which airline online L3 by using this equation that I could be = 2 x 3 + 2 Lander 3 and why would be equal to y 3 - 2 Lander 3 Android good B equals to Z 3 - of Lambda 3 right now we have this thing now how do we use this thing we know that point see this point |

06:00 - 06:59 | is a common point of Intex intersection of line L1 and L2 re so we can say that this point she will have the having the coordinates as extra coronavirus 3commas z3 is going to lie on a line L1 also writes it is going to satisfy the equation of a line as and also write and we know that this line L1 is having this equation and if three coronavirus 33 that is point C satisfies the equation of this line then when we put the value of x 3 Y is y3 and that is that three sons going to satisfy this right to we are going to use the equation of x 3 by 3 and 3 in this line and substitute the rally was so finally when we substitute the values of X Y and Z in L3 this could be X equals to instead of three were going to write it 7 - 3 Lambda oneplus 2 landed 3 right now |

07:00 - 07:59 | going to use the same equation that is this equation for y83 so why would be equals to y3 that is equal to 3 + Lambda 2 - of 23 again we can use the same principle to find the value of Z that would be equal to 3 and the tree is equals to 2 + 4 land the one and this is -3 right now via optane the values of x y z which are the coordinates of point which is lying on a line l 3 in terms of London London 3 right now we know that point that is this point it is this one that is point the is a point which is having these coordinates and is lying on a line and 2 and 3 respectively right so we can say that this point the when put in the equation of line L2 is going to satisfy that equation also so we can say that if this line L2 is having a point the existing on it then the cord |

08:00 - 08:59 | 8 4.64 cover vi Pur Z4 would be given by this equation only right and we know that this point the is lying at l-3 at the same time right and this point if lying on the line L3 and the coordinates of the point which is lying on l 3 is having these values that we can say that they should be equal to the coordinates of point that a given by X 4 cover by 484 right so we can say that this value of x would be equal to X 4 which is actually equal to 7 - 3 x Lambda 1 + 2 X Lander 3 and instead of this X4 we are going to write the value of this export right so finally what we obtain is the three equations which are actually x 4 = 2 x 4 equal to this and this exposes been replaced by the soldiers will be 5 + 2 lehenga to equal to 7 - 3 grander 1 |

09:00 - 09:59 | 23 this is one equation another equation is coronavirus for this is going to be vi Pur and this why is same as the survivors we can say that 3 + Lambda to is equal to 3 + Lambda 2 - of Lambda to London 3 right right now there is a correction in this actually 6 plus to London flights this is 6 plus two level there is a correction if this is 6211 and now it is going to be a correct equation if we correct this this is basically 6 plus two level 86 plus 2 Lander 1 - 23 right now we have to write the value for Z4 using this equation and this equation right so we can say that 4 plus 3 landour to should be equal to 2 + Lambda 1 - of langur 3 flight |

10:00 - 10:59 | now what are you going to do we are going to solve this equation to find the value for Lambda 102 and 103 respectively the first of all latest real fuse equations we can say that really I'm the one mind cylinder 1 + 2 Lander 2 - 2 Lander 3 is equals to to write if you are a second equation that after hearing this would be to land the 1 - lehenga to -2 langur 3 equals to minus 3 and after realising the third equation view 10 400001 -3 Lander 2 - of Lambda 3 that is equal to 2 right now we have to solve the values of 11 lehenga to Atlanta 3 so for that what are you going to do if we subtract the value of this equation from the situation plan view of the five Lambda this is Lambda event and this could be plus of three Lambda to write this is going to be something like |

11:00 - 11:59 | Ahmedabad 1 minus 10 plus of three Lambda to and thus becomes = 25 right after that what are you going to do if you multiply this equation by two on both sides equation becomes 8 Lambda 1 - 6 lehenga to -2 langur 3 equals to 4 and another equation which we have is to Lambda 1 - Lambda to -2 langur 3 equals to minus 3 and if we subtract the value of the situation from the situation that what can finally Octane is Sikh calendar 1985 langda to that is equal to 7 right now we have to solve this equation is also so when we take this week Nation and if we multiply the first equation by 6 and what we obtain is Sikander 1 + 18 langur 2 equals to 30 second equation remains as it is that a 6 November 1 - 5 = 27 |

12:00 - 12:59 | so when we subtract the value of this equation from this equation than what we obtain is a value for Lambda to so that would be 23 Lambda to equals to 23 then find the value of 2 comes out to be equal to 1 now we're hoping the value for Lambda to right now we have to obtain the value for land and also so if you put the value of Lambda to equals to 1 in this equation that we can find the value column 1 so Lambda oneplus 3 into one would be equal to 5 if we can say that London 1 is equals to 2 becomes a value for London right now we have over the value for London 32 if you use any of the equation that it's a we use this equation than I can say that school in 22 - of 3 into 1 minus 3 is equal to 2 so we can say that it - 3 = 25 - 2 = 23 becomes a value for land that research laboratory becomes equal to |

13:00 - 13:59 | now we obtain the value of all under one langot wale and 3 respectively so we can easily calculate the points are the coordinates of the point that are required to satisfy the coordinates of point c and coordinates of point d c we know the coordinates of point C which are given by 7 - Sri Lanka 16 + William the 1 and 2 + Poland David like we're going to use is equation to find the coordinates of point see when X is given by Y is given by that is given by so we have to use these equations write the first equation is 7 - 3 cylinder 17 - 3 langda 1 second equation is 6 plus to London flight second equation is 6 + 11 and third equation is two plus 4 level SO2 + Poland can also find the value for the coordinates of point the right so this would be x = 2y = 2 Z = 2 and we are going to use the situation that is |

14:00 - 14:59 | 25 + 2 langur 23 + Lambda to and coldness freelander 2 to 5 + 2 Lander 23 + lehenga to and this is for + 22 + Sri Lanka 2004 plus 3 Nanda to light and now we know the value of Lambda one that is equal to what to do this value becomes equal to 1 this study is equals to 10 and the study also becomes equal to text right now we have to find the value of x y z for point they also when we know the value of Lambda to as equals to 1 so the first value becomes 7 this is equal to 4 and this allows it was 27 now finally we need to evaluate the value of a vector for a b vector we need to know the coordinates of point a and the coordinates of point AR 762 and coordinates of Point Dr 45434 right so a b vector is equals to what a vector becomes -2 |

15:00 - 15:59 | - 3 - 2 - 3 comedy to write similarly we need to find the value of tractor AC sweater AC would be equal to what it is -64 comma it right and now we have to find the value for vector area also sweater aidi would be equal to should be equal to 0 - 25 flight so now we have obtained the value of these vectors and now we need to find the volume of the barrel of 5 what is bound by these three Rakta so how can we find obviously by using the method of determining that is -2 -3 and this is to this is -6 this is for this is 8 and this is zero is -2 and this is 5 right so we need to solve the value of this one so when we solve this could be come out as minus 2 into 450 20 - of -16 that becomes + 16 right |

16:00 - 16:59 | - 2 - 3 x + 3 that should be x minus 30 and + 2 should be X + 12 right now we have obtained the value of this expression - 72 - 90 + 20 ko this comes out to be -138 now we know since this figure is actually of a volumes and thus cannot be negative value it comes out to be 138 finally now we have figured out the volume of the parallel pipe has been formed by the three factors and option to become the most appropriate answer for the given problem |

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