If `vec a` is perpendicular to `vec b` and `p` is non zero scalar such that `pbar(r)+(bar(r).bar(b))bar(a)=bar(c)`

If bar(a), bar(b), bar(c) are non-coplanar vectors and x, y, z are scalars such that bar(a)=x(bar(b)timesbar(c))+y(bar(c)timesbar(a))+z(bar(a)timesbar(b)) then x =

If bar(a),bar(b),bar(c) are position vectors of vertices A,B,C of Delta ABC. If bar(r) is position vector of apoint P such that (|bar(b)-bar(c)|+|bar(c)-bar(a)|+|bar(a)-bar(b)|)bar(r)=|bar(b)-bar(c)|bar(a)+|bar(c)-bar(a)|bar(b)+|bar(a)-bar(b)|bar(c) then the point P is

If bar(a) is perpendicular to bar(b) then bar(a)*bar(b) is

If bar(a),bar(b),bar(c) and bar(p),bar(q)bar(r) are two sets of three non- coplanar vectors such that bar(a)*bar(p)+bar(b).bar(q)+bar(c).bar(r)=3 then bar(P)=.......bar(q)=......,bar(r)=......

If bar(a),bar(b),bar(c) are three non zero vectors,then bar(a).bar(b)=bar(a).bar(c)rArr

Let bar(a),bar(b) and bar(c) be non-zero and non collinear vectors such that (bar(a)times bar(b))times bar(c)=(1)/(3)|bar(b)||bar(c)|bar(a) .If theta is the acute angle between the vectors bar(b) and bar(c) then sin theta

Three non - zero vectors bar(a),bar(b),bar(c) are complanar if and only if there exist scalars x,y,z, not all zero simultaneously such that xbar(a)+ybar(b)+zbar(c)=bar(0) .

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.

If bar(p) and bar(s) are not perpendicular to each other and bar(r)xxbar(p)=bar(q)xxbar(p)o*bar(r).bar(s)=0, then bar(r) is