Home/ Questions/Q 427313
Next
In Process
Radheshyam Narula
Asked: 2022-11-02T11:52:37+05:30 In:

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.

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.
Parabola
Leave an answer

Leave an answer

Browse

1 Answer

  1. `:.` 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^(@)`.

    • 0