Given the position vectors of three points `A(hati-hatj+2hatk ),B(4hati+5hatj+8hatk) and C(3hati+3hatj+6hatk)` . Prove that A,B and C are collinear.

Given the position vectors of three points A(hati-hatj+2hatk ),B(4hati+5hatj+8hatk) and C(3hati+3hatj+6hatk) . Find the projection of vec(AB) on vec(AC) .

Show that the points A(-2 hati+3 hatj+5 hatk) , B(hati+2 hatj+3 hatk) and C(7 hati-hatk) are collinear.

The direction cosines of the vector hati-5hatj+8hatk are

Show that the points with position vectors 2hati+6hatj+3hatk,hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

Find the sum of the vectors. veca=hati-2 hatj+hatk, vecb=-2 hati+4 hatj+5 hatk and vecc=hati-6 hatj-7 hatk

Show that the points with position vectors '2 hati+6 hatj+3 hatk, hati+2 hatj+7 hatk' and '3 hati+10 hatj-hatk' are collinear.

Show that the vectors 2 hati-hatj+hatk, hati-3 hatj-5 hatk and 3 hati-4 hatj-4 hatk form the vertices of a right-angled triangle.

Find the position vector of the point where the line vec r = hati - hatj +hatk + t (hati + hatj -hatk ) meets the plane vecr. (hati + hatj + hatk ) =5

Show that the vectors 2 hati-3 hatj+4 hatk and -4 hati + 6 hatj-8 hatk are collinear.