`P,Q,R,S` have position vectors `bar p,bar q,bar r,bar s` respctively such that `(bar p-bar q)=2(bar s-bar r)` then `QS` and `PR`

P, Q, R, S have position vectors bar(p), bar(q), bar(r), bar(s) respectively such that (bar(p)-bar(q))=2(bar(s)-bar(r)) , then QS and PR

For three vectors bar(p), bar(q) and bar(r)" if "bar(r)=3bar(p)+4bar(q) and 2bar(r)=bar(p)-3bar(q) then

The vectors bar X and bar Y satisfy the equations 2bar X =bar p,bar X+2bar Y =bar q where bar p=bar i+bar j and bar q=bar i-bar j. If theta is the angle between bar X and bar Y then

In the space A(bar(a)) is a point and bar(b) is a vector. If P(bar(r )) is any point such that bar(r ) xx bar(b) = bar(a) xx bar(b) then show that locus of P is a straight line.

Let bar(a)=-bar(i)-bar(k),bar(b)=-bar(i)+bar(j) and bar(c)=bar(i)+2bar(j)+3bar(k) be three given vectors. If bar(r) is a vector such that bar(r) times bar(b)=bar(c) times bar(b) and bar(r).bar(a)=0 then bar(r).bar(b)=