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.

Options

A. `pi/2`
B. `pi/4`
C. `pi`
D. None of these

Answer

C

Explanation

Here, coordinates of the points A,B,C and D be (1,2,3), (4,5,7),(-4,3,-6) and (2,9,2) respectively
`therefore` Direction rations of line AB are
(4,-1,5-2,7-3) or (3,3,4)
Direction ratios of line CD are
(2+4,9-3,2+6) or (6,6,8)
Let the direction ratios of AB and CD are `a_1,b_1,c_1 and a_1b_2,c_2` respectively
`therefore" "a_1/a_2=3/6=1/2,b_1/b_2=3/6=1/2,c_1/c_2=4/8,=1/2`
It can be seen that `a_1/a_2=b_1/b_2=c_1/c_2`
Therefore, AB is parallel to CD
Thus, the angle betweeen AB and CD is either `0^@ or 180^@`