The position vector of two points A and B are `3veci+vecj+2veck and veci-2vecj-4veck` respectively. Find the equation of the plane through B and perpendicular to AB.

The position ector sof points P,Q,R are 3veci+4vecj+5veck, 7veci-veck and 5veci+5vecj respectivley. If A is a point sequidsictnat form the lines OP, OQ and OR find a unit vector along vec(OA) where O is the origin.

Position vectors of two points A and C re 9veci-vecj+7veci-2vecj+7veck respectively THE point intersection of vectors vec(AB)=4veci-vecj+3veck and vec(CD)=2veci-vecj+2veck is P. If vector vec(PQ) is perpendicular to vec(AB) and vec(CD) and PQ=15 units find the position vector of Q.

A rigid body is rotating at 5 radians per second about an axis AB where A and B are the pont 2veci+vecj+veck and 8veci-2vecj+3veck respectively. Find the veclocity of the practicle P of the body at the points 5veci-vecj+veck .

Let veca=2veci+3vecj+4veck and vecb=3veci+4vecj+5veck . Find the angle between them.

Find the angle between veca=3veci+3vecj-3veck and vecb=2veci+vecj+3veck .

Find the set of vectors reciprocal to the set of vectors 2veci+3vecj-veck, veci-vecj-veck, -veci+2vecj+2veck

Show that the vectors veci-3vecj+2veck, 2veci -4vecj-veck and 3veci+2vecj-veck are linearly independent.

Write the unit vector in the direction of vecA=5veci+vecj-2veck .

The position vectors of the points A,B,C,D are vec(3i)-vec(2j)-veck, vec(2i)+vec(3j)-vec(4k)-veci+vecj+vec(2k) and vec(4j) +vec(5j)+vec(lamdak) respectively Find lamda if A,B,C,D are coplanar.

A unit vector coplanar with veci + vecj + 2veck and veci + 2 vecj + veck and perpendicular to veci + vecj + veck is _______