`P ,Q` have position vectors ` vec a& vec b` relative to the origin `' O^(prime)&X , Ya n d vec P Q` internally and externally respectgively in the ratio `2:1` Vector ` vec X Y=` a.`3/2( vec b- vec a)` b. `4/3( vec a- vec b)` c. `5/6( vec b- vec a)` d. `4/3( vec b- vec a)`

The position vector of A,B are vec a and vec b respectively.The position vector of C is (5(vec a)/(3))-vec b then

If vec p = vec a + vec b, vec q = vec a-vec b | vec a | = | vec b | = 1 then | vec p xxvec q | =

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

If two vectors vec a and vec b are such that |vec a|=2,|vec b|=1 and vec a*vec b=1, find (3vec a-5vec b)*(2vec a+7vec b)

vec aa n d vec b are two unit vectors that are mutually perpendicular. A unit vector that is equally inclined to vec a , vec ba n d vec axx vec b is a.1/(sqrt(2))( vec a+ vec b+ vec axx vec b) b. 1/2( vec axx vec b+ vec a+ vec b) c. 1/(sqrt(3))( vec a+ vec b+ vec axx vec b) d. 1/3( vec a+ vec b+ vec axx vec b)

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b-vec c and 4vec a-7vec b+7vec c are collinear.

Show that the points whose position vectors are vec(a) + 2vec(b) + 5vec(c), 3vec(a) + 2vec(b) + vec(c), 2vec(a) + 2vec(b) + 3vec(c) are colliner.

If vec a and vec b are two vectors,such that |vec a|=2,|vec b|=1 and vec a*vec b=1, then find (3vec a-5vec b)*(2vec a+7vec b)

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

Show that the point A,B,C with position vectors vec a-2vec b+3vec c,2vec a+3vec b-4vec c and -7vec b+10vec c are collinear.