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 A (6,-6,0), B(-1,-7,6), C (3,-4, 4) and D (2,-9,2) be four points in space. Show that AB is perpendicular to CD.

If A(4,8,12), B(2,4,6), C(3,5,4) and D(5,8,5) are four points, show that the lines vec(AB) and vec(CD) intersect.

If the co-ordinates of four points in space are A(6,-6,0), B(-1,-7,6), C(3,-4,4) and D(2,-9,2) then show that AB is perpendicular to CD.

A(1, -2, 4), B(5, -1, 7), C(3, 6, -2) and D(4, 5, -1) are given vectors. Then the projection of vec(AB) on vec(CD) is ……………

If A(8,2,0),B(4,6,-7),C(-3,1,2)and D(-9,-2,4) are four given point then find the angle between vec(AB)and vec(CD) .

If A(2, -1, 4), B(0, 1, 5), C(4, 3, 5), D(6, 4, 3) then the projection of bar(AB) " on " bar(CD) is

If A ,B ,C ,D are four distinct point in space such that vec(A B) is not perpendicular to vec(C D) and satisfies vec (A B).vec (C D)=k(| vec(A D)|^2+| vec(B C)|^2-| vec(A C)|^2-| vec(B D)|^2), then find the value of kdot

If A ,B ,C ,D are four distinct point in space such that vec(A B) is not perpendicular to vec(C D) and satisfies vec (A B).vec (C D)=k(| vec(A D)|^2+| vec(B C)|^2-| vec(A C)|^2-| vec(B D)|^2), then find the value of kdot

If A = (-2, 3, 4), B = (-4, 4, 6), C = (4, 3, 5), D = (0, 1, 2) then the projection of AB on CD is

Let A(2,3,4),B(4,3,2) and C(5,2,-1) be three points .Find the projection of vec(BC) on vec(AB) .