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

The position vectors of P and Q are respectively vec a and vec b . If R is a point on vec(PQ) such that vec(PR) = 5 vec(PQ), then the position vector of R, is

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.

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.

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

Prove that the four points 4veci+5veci+veck, -(vecj+veck),3veci+9vecj+4veck and 4(-veci+vecj+veck) are coplanar

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

Let points P,Q, and R hasve positon vectors vecr_1=3veci-2vecj-veck, vecr_2=veci+3vecj+4verck and vecr_3=2veci+vecj-2veck relative to an origin O. Find the distance of P from the plane OQR.

If vecA=2veci-3vecj+7veck, vecB=veci+2veck and vecC=vecj-veck find vecA.(vecBxxvecC) .

If O is origin annd the position vector fo A is 4hati+5hatj , then unit vector parallel to OA is

The position vectors of points A and B w.r.t. the origin are veca=hati+3hatj-2hatk and vecb=3hati+hatj -2hatk , respectively. Determine vector vec(OP) which bisects angle AOB , where P is a point on AB.