O is the origin , P(2,3,4), Q(1,k,1) are points such that `bar(OP) _|_ bar(OQ)` then find k.

O is the origin, P(2,3,4) and Q(1,k,1) are points such that bar(OP)botbar(OQ). Find k.

If O is the origin and P=(2, 3), Q=(4, 5) then OP*OQ cos angle POQ=

If O is the origin and P = (1, -2, 1) and OP bot OQ , then Q =

Let bar(a) = 2bar(i)-bar(j)+bar(k), bar(b) = 3bar(i) + 4bar(j) -bar(k) and if theta is the angle between bar(a), bar(b) then find sin theta .

In DeltaOAB , L is the midpoint of OA and M is a point on OB such that (OM)/(MB)=2 . P is the mid point of LM and the line AP is produced to meet OB at Q. If bar(OA)=bar(a), bar(OB)=bar(b) then find vectors bar(OP) and bar(AP) interms of bar(a) and bar(b) .

If O is origin, and P = (1, -2, 1) and OP _|_ OQ then Q =

If P(-2,4,-5) and Q(1,2,3) are two points. Find the direction cosines of bar(PQ)