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.

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 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.

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

Find the dot and cross product of the vectors veca=2veci-3vecj+veck and vecb= -veci+3vecj+veck

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

Find the direction cosines and unit vector along the vector vecr=2veci+vecj+3veck .

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

if vec b=2 vec i + 3 vec j - vec k and vec c= vec i + 4 vec j + 5 veck then find a vector vec a such that vec b * vec a =0 and vec c * vec a=0 . Also find the unit vector along vec a .