Find x such that the four points A(3,2,1)B(4,x,5),C(4,2,-2)and D(6,5-1)are coplanar.

Prove that the points (2,4,4),(1,5,4),(2,6,2)and (0,6,4) are coplanar.

Find the value of lambda if the points. A(-1,4,-3),B(3, lamda,-5),C(-3,8,-5) and D(-3,2,1) are coplanar.

If A, B, C, D are the points (3,4,5),(4,6,3),(-1,2,4) and (1,0,5) , find the angle between C D and A B

If the co-ordinates of the points A, B, C, D be (1,2,3),(4,5,7) (-4,3,-6) and (2,9,2) respectively, then find the angle between the lines AB and CD

Find x and y satisfying the matrix equation [(x-y,2,-2),(4,x,6)] + [(3,-2,2),(1,0,-1)] = [(6,0,0),(5,2x+y,5)]

Find the equation of the planes that pass through the points.. (1, 1, -1), (6, 4, -5), (-4, -2, 3)

Find the equation of the plane passing through the points (3,-1,2) , (5,2,4) ,(-1,-1,6)

Show that the line AB is perpendicular CD if A,B,C,D are the points (2,3,4),(5,4,-1),(3,6,2),(1,2,0) respectively.

The nearest point on the line x + y - 3 = 0 from the point (3, -2) is a)(3, 5) b)(4, 1) c)(3, -5) d)(4, -1)

Given the vertices A(2,-1,4), B(3,2,-6) and C(-5,0,2) of a triangle ABC Find the mid point of BC