If A(2, -5), B(-2, 5), C(x, 3) and D(1, 1) be four points such that AB and CD are perpendicular to each other, find the value of x.

If A(2, 3, 4), B(5, 4, -1), C(3, 6, 2) and D(1, 2, 0) be four points, show that vec(AB) is perpendicular to vec(CD) .

If the points A(1,3) , B(-2,1) , C(x,2) and D(-1,5) are given and AB is perpendicular to CD , find the value of x .

If the points A(1,3) , B(-2,1) , C(x,2) and D(-1,5) are given and AB is perpendicular to CD , find the value of x .

A(2, 3), B(-1, 5), C(-1, 1) and D(-7, 5) are four points in the Cartesian plane. Check if, bar(CD) is parallel to bar(AB) .

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.

Let A(-2, 0, 3), B(0, 3, -3), C(3, 3, 5) and D(5, 4, 3) be four given points, find the acute angle between the lines AB and CD.

Consider the 4 points A(3, 2, 1) B(4, x, 5) C(4, 2, -2) and D(6, 5, -1) (i) Find vec(AB) , vec (AC) and vec(AD) . (ii) If the points A, B, C and D are coplanar, find the value of x.

If the lines (x-1)/(-3) =(y-2)/(2lambda) =(z-3)/(2) " and " (x-1)/(3lambda) =(y-1)/(1)=(6-z)/(5) are perpendicular to each other then find the value of lambda