InterviewSolution
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InterviewSolution
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If the coordinates of the points `A,B,C,D be 91,2,3),(4,5,7),(-4,3,-6) and (2,9,2)` respectively then find the angle between AB and CD. |
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Answer» `:.` Direction ratios of AB `(4-1),(5-2),(7-3)= (3,3,4)` Direction ratios of CD `(2+4),(9-3),(7-3)=(3,3,4)` Direction of CD `(2+4),(9-3),(2+6)=(6,6,8)` Let the directi on ratios of AB and CD are `(a_(1),b_(1),c_(1))` and `(a_(2),b_(2),c_(2))` respectively. Then, `(a_(1))/(a_(2)) = 3/6 = 1/2 , (b_(1))/(b_(2)) = 3/6 = 1/2 , (c_(1))/(c_(2)) = 4/8 = 1/2` `(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))` `:. (a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))` Therefore, line AB is parallel to line CD, so the angle between AB and CD is `0^(@)`. |
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