Let `hat a and hat c` be unit vectors at an angle `pi/3` with each other.If `(hat a xx (vec b xx vec c))*(hat a xx hat c)=5` then the value of `[hat a vec b hat c]` is

Let vec a,vec b,vec c and are unit vectors inclined to each otherat an angle of (2 pi)/(3). If hat p,hat q and hat r are unit vectors alongthe angle bisectors of vec a and vec b,vec b and vec c and vec a are spectively, then [hat phat qhat r] is equal to

Let vec a = hat i + hat j + hat k, vec b = hat i + 4 hat j - hat k, vec c = hat i + hat j + 2 hat k and hat s be a the unit vector the magnitude of the vector (vec a .vec s)(vec b xx vec c) + (vec b. vec s)(vec c xx vec a) + ( vec c.vec s)(vec a xx vec b) is equal to (A) 1 (B) 2 (C) 3 (D) 4

Let hat a , hat b , hatc be unit vectors such that hat a * hatb =hat a *hatc =0 and the angle between hat b and hat c be (pi)/(6) prove that hat a =+- 2 (hatb xx hat c )

For any vector vec a , prove that hat i xx (vec a xx hat i)+ hat j xx (vec a xx hat j) + hat k xx(vec a xx hat k)= 2 vec a

Let vec(a) = - hat(i) - hat(k) , vec(b) = - hat(i) +hat(j) and vec(c) = hat(i) + 2hat(j) + 3 hat(k) be three given vectors . If vec(r ) is a vector such that vec(r ) xx vec(b) = vec (c ) xx vec(b) and vec (r ) . vec (a ) = 0 then the value of vec(r ). vec(b) is -

If vec a=hat j-hat k and vec c=hat i+hat j+hat k are given vectors,and vec b is such that a vec a*vec b=3 and vec a xxvec b+vec c=0 then is equal to

If vec(a) = 3 alpha hat(i) + 2hat(j) - 3 hat (k) , vec(b) = hat(i) + 6 alpha hat(j) - 2 hat(k) and hat (c ) = 2 hat(i) - 3 alpha hat(j) + hat(k) be such that {(vec(a) xx vec(b))xx (vec(b) xx vec(c)) } xx (vec(c) xx vec(a)) = vec(O) , then the value of 9 alpha is -

Let hat(a) , hat(b) " and " hat( c) be three unit vectors such that hat(a) xx (hat(b) xx hat( c)) = (sqrt(3))/(2)( hat(b) +hat(c )). If hat(b) is not parallel to hat( c) then the angle between hat(a) " and " hat(b) is

Let hat(a) , hat(b) " and " hat( c) be three unit vectors such that hat(a) xx (hat(b) xx hat( c)) = (sqrt(3))/(2)( hat(b) +hat(c )). If hat(b) is not parallel to hat( c) then the angle between hat(a) " and " hat(b) is

If vec a=hat i+2hat j-2hat k,vec b=2hat i-hat j+hat k and vec c=hat i+3hat j-hat k then find vec a xx(vec b xxvec c)