`A(0,5,6),B(1,4,7),C(2,3,7) and D(3,4,6)` are four points in space. The point nearest to the origin `O(0,0,0)` is (A) A (B) B (C) C (D) D

The distance of the point P(4,\ 3) from the origin is (a) 4 (b) 3 (c) 5 (d) 7

The distasnce of the plane 2x-3y+6z+14=0 from the origin is (A) 2 (B) 4 (C) 7 (D) 11

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.

Using vectors show that the points A(-2,3,5), B(7,0,-1), C(-3,-2,-5) and D(3,4,7) are such that AB and CD intersect at the point P(1,2,3).

Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6) and D(2,-5,10) are such that AB and CD intersect at the point P(1,-1,2) .

The coordinates of the point equidistant from the points A(0, 0, 0), B(4, 0, 0), C(0, 6, 0) and D(0, 0, 8) is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. Q. The perpendicular distance of D from the plane ABC is

Find the coordinates of a point equidistant from the origin and pints A(a ,0,0),\ B(0, b ,0)a n d\ C(0,0, c)dot

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the line L is