If A, B, C and D are four points with position vectors `3hati, 3hatj, 3hatk` and `hati+hatj+hatk` respectively, then D is the

If A, B, C and D are the points with position vectors hati+hatj-hatk,2hati-hatj+3hatk,2hati-3hatk and 3hati-2hatj+hatk respectively, then find the projection of vec(AB) along vec(CD) .

The values of a for which the points A, B, and C with position vectors 2hati - hatj + hatk, hati - 3hatj - 5hatk, and ahati - 3hatj + hatk ,respectively, are the vertices of a right-angled triangle with C = pi/2 are

If A,B,C,D are the points with position vectors : hati+hatj-hatk,2hati-hatj+3hatk,2hati-3hatk,3hati-2hatj+hatk respectively, find the projection of vec(AB) along CD.

Show that the four points A,B,C and D with position vectors 4hati+5hatj+hatk, -hatj-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk) respectively, are coplanar.

Consider points A,B,C and D with position vectors 7hati-4hatj+7hatk, hati-6hatj+10hatk, hati-3hatj+4hatk and 5hati-hatj+5hatk respectively. Then ABCD is a (A) square (B) rhombus (C) rectangle (D) parallelogram but not a rhombus

If the four points with position vectors -2hati+hatk, hati+hatj+hatk, hatj-hatk and lamda hatj+hatk are coplanar then lamda= (A) 1 (B) 2/3 (C) -1 (D) 0

If the position vectors of the points A, B, C, D are hati+hatj+hatk, 2hati+5hatj, 3hati +2hatj-3hatk and hati-6hatj-hatk respectively, then the angle between the vectors vec(AB) and vec(CD) is -

Are the points A ,B and C with position vectors -2hati + 3hatj + 5hatk, hati + 2hatj + 3hatk and 7 hati - hatk respectively collinear ?

Show that the four points A,B,C and D with position vectors 4hati+5hatj+hatk,-(hatj+hatk),(3hati+9hatj+4hatk) and 4(-hati+hatj+hatk) respectively are coplanar.