Prove that the vectors `3 vec I + 5 vec j + 2 vec k, 2 vec I - 3 vec j - 5 vec k` and `5 vec I + 2 vec j -3 vec k` form the sides of an equilatera, triangle.

| 2vec i-3vec j + vec k | =

(vec i + xvec j + 3vec k) xx (vec i-vec j + vec k) = 5vec i + xvec j-3vec k then x =

if the vectors vec a=vec i+vec j+vec k, , b=vec i-vec j+2vec k and vec c=xvec i+(x-2)vec j-vec k are coplanar then x is

The position vectors of three points are vec i+3vec j-2vec k,3vec i-2vec j+vec k and -2vec i+vec j+3vec k show that the points are the vertices of an equilateral triangle

The vectors of A,B,C and D are respectively 2 vec I + 3 vec j + 5 vec k, vec I + 2 vec j + 3 vec k, -5 vec I + 4 vec j - 2 vec k and vec I + 10 vec j + 10 vec k . Show tthat AB and CD are parallel.

The value of 'a',for which the points A,B,C with position vectors 2vec i-vec j+vec k+vec k,vec i-3vec j-5vec k, and avec i-3vec j+vec k are vertices of a right angled triangle with /_C=(pi)/(2) are

The values of a for which the points A,B,C with position vectors 2vec i-vec j+vec k+vec i-3vec j-5vec k and avec i-3vec j+vec k,vec i-3vec j-5vec k and avec i-3vec j+vec k are the vertices of a right angled triangle with /_C=(pi)/(2) are

vec a = -vec i + vec k and vec b = 2vec j-vec k are the underset aa = -vec i + vec k and vec b = 2vec j-vec k are the adjacent sides of a paralellogram then its vector area is

Find the value of: (vec j xxvec k) * (3vec i + 2vec j-vec k)

If | vec a | = 2, | vec b | = 7 and vec a xxvec b = 3vec i + 2vec j + 6vec k then vec a * vec b =