If A(1, 2, 3), B(4, 5, 7), C(-4, 3, -6) and D(2, 9, 2) are four given points then find the angle between the lines AB and CD.

Given -

A = (1,2,3)

B = (4,5,7)

C = (-4,3,-6)

D = (2,9,2)

Formula to be used – If P = (a,b,c) and Q = (a’,b’,c’),then the direction ratios of the line PQ is given by ((a’-a),(b’-b),(c’-c))

The direction ratios of the line AB can be given by

((4-1),(5-2),(7-3))

=(3,3,4)

Similarly, the direction ratios of the line CD can be given by

((2+4),(9-3),(2+6))

=(6,6,8)

To find – Angle between the two pair of lines AB and CD

Tip – If (a,b,c) be the direction ratios of the first line and (a’,b’,c’) be that of the second, then the angle between these pair of lines is given by

The angle between the lines