If `p hati+q hatj+r hatk` is vector along a line, then p, q, r are

Given: vec p = - hati -3 hatj + 2hatk and vec r = hati + 3 hatj + 5hatk . Find vector parallel to electric field at position r. [ Note that vec p . vec r = 0 ]

If the vectors p hati + hatj+ hatk, hati i+ q hatj + hatk and hati + hatj + r hatk ( p ne q ne r ne 1) are coplanar, then the value of pqr- (p + q + r) is :

A vector vec P when added to the sum of the vectors 2hati-3hatj+hatk and -3hati-hatj+hatk gives a unit vector along the x-axis. What is the magnitude of the vector vec P ?

The position vectors of the points P and Q are 5hati+ 7hatj- 2hatk and -3hati+3hatj+6hatk , respectively. Vector vecA= 3hati-hatj+hatk passes through point P and vector vecB=-3hati+2hatj+4hatk passes through point Q. A third vector 2hati+7hatj-5hatk intersects vectors A and B. Find the position vectors of points of intersection.

The position vectors of the points P and Q are 5hati+ 7hatj- 2hatk and -3hati+3hatj+6hatk , respectively. Vector vecA= 3hati-hatj+hatk passes through point P and vector vecB=-3hati+2hatj+4hatk passes through point Q. A third vector 2hati+7hatj-5hatk intersects vectors A and B. Find the position vectors of points of intersection.

If P, Q, R are three points with respective position vectors hati + hatj, hati -hatj and a hati + b hatj + c hatk . The points P, Q, R are collinear, if

If P, Q, R are three points with respective position vectors hati + hatj, hati -hatj and a hati + b hatj + c hatk . The points P, Q, R are collinear, if

If the vectors phati+hatj+hatk,hati+qhatj+hatk and hati+hatj+rhatk(p ne q ne r ne 1) are coplanar, then the value of pqr-(p+q+r) is :