consider the points A, B and C with position vectors `(-2hat i+3hatj+5hatk),(hati+2hatj+3hatk)` and `7hati-hatk` respectively.statement -1: The vector sum, `vec(AB)+vec(BC)+vec(CA)=vec0`

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) .

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

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 -

The position vectors of the vertices of /_\ABC are : 3hati-4hatj-4hatk,2hati-hatj+hatk and hati-3hatj-5hatk respectively. Find vec(AB),vec(BC) and vec(CA) .

The position vectors of the points A, B, C and D are hati+3hatj-hatk, -hati-hatj+hatk, 2hati-3hatj+3hatk and -3hati+2hatj+hatk respectively. Then, the ratio of the moduli of the vectors vec(AB) and vec(CD) is -

Show that the points A, B and C with position vectors, vec(a)=3hati-4hatj-4hatk,vec(b)=2hati-hatj+hatk and vec( c )=hati-3hatj-5hatk , respectively form the vertices of a right angled triangle.

Dot product of a vector vec(a) with hati+hatj-3hatk,hati+3hatj-2hatk and 2hati+hatj+4hatk are 0, 5 and 8 respectively. Find the vector.

If the position vectors of the point A and B are : 7hati+3hatj-hatk and 2hati-5hatj+4hatk respectively, find the magnitude and direction-cosines of the vector vec(AB) .

If the verticles of a tetrahedron have the position vectors vec0, hati+hatj, 2hatj-hatk and hati+hatk then the volume of the tetrahedron is

If the verticles of a tetrahedron have the position vectors vec0, hati+hatj, 2hatj-hatk and hati+hatk then the volume of the tetrahedron is