If P(1,2,-3) and Q(4,3,5) are two points in space , find the direction ratio of `vec(OP),vec(QO)` and `vec(PQ)`.

If P(2,3,-6) and Q(3,-4,-6) are two points in the space. Find the direction cosines of vec(OP),vec(QO) and vec(PQ) , where Q is the origin.

If A(1,2,-3) and B(-1,-2,1) are the two given points in space then find (i) the direction ratios of vec(AB) and (ii) the direction cosines of vec(AB) . Express vec(AB) in terms of hati , hatj and hatk .

If P(2,-1,4) is a point in the space, find the direction cosines of vector vec(OP)

If P(1,2,3) and Q(2,-1,4) are two points then |vec(PQ)| is equal to

If P(1,2,3) and Q(-1,0,3) are two points then vec(PQ) is equal to

If P(1,2,3) and Q(-1,0,3) are two points,then vec(PQ) is equal to

If P(1,2,3) and Q(2,-1,4) are two points,then |vec(PQ)| is equal to

If P-=(1,5,4) and Q-=(4,1,-2) find the direction ratios of vec(PQ)

If P(-1,2) and Q(3,-7) are two points, express the vectors vec(PQ) in terms of unit vectors hatiand hatj . Also find the distance between points P and Q. What is the unit vector in the direction of vec(PQ) ? Verify that magnitude of unit vector indeed unity.

A charge Q located at a point vec r is in equilibrium under the combined field of three charges q_(1), q_(2) and q_(3) . If the charges q_(1) and q_(2) are located at point vec r_(1) and vec r_(2) respectively, find the direction of the force on Q due to q_(3) in terms of q_(1),(q_2), vec r_(1) vec r_(2) , and vec(r) .