Let `veca,vecb,vecc` be three non-zero vectors such that `vec(c)` is a unit vector perpendicular to both `vec(a)andvec(c).` If the angle between `vec(a)andvec(c)" is "(pi)/(6)," show that "[vec(a),vec(b),vec(c)]^(2)=(1)/(4)absvec(a)^(2)absvec(b)^(2).`

Let vec a = a_1 hat i + a_2 hat j+ a_3 hat k;vec b = b_1 hat i+ b_2 hat j+ b_3 hat k ; vec c= c_1hat i + c_2 hat j+ c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec a & vec b . If the angle between vec a and vec b is pi/6 , then |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|^2=

The non-zero vectors vec a , vec b and vec c are related by vec a=8 vec b and vec c = −7 vec b , then the angle between vec a and vec c is

If vec(a),vec(b),vec(c) are three unit vectors such that vec(a) is perpendicular to vec(b) , and is parallel to vec(c) then vec(a)xx(vec(b)xxvec(c)) is equal to

If vec(a),vec(b),vec(c) are three non-coplanar vectors such that vec(a)xx(vec(b)xxvec(c))=(b+c)/(sqrt(2)), then the angle between vec(a)andvec(b)" is "

If vec(a)andvec(b) are unit vectors such that [vec(a),vec(b),vec(a)xxvec(b)]=(pi)/(4)," then the angle between "vec(a)andvec(b)" is "

If veca ,vecb, vec c are three vectors such that veca + 2 vecb + vecc = vec0, and |veca|=3, |vecb|=4, |vec c|=7, find the angle between vec a and vecb.

Let vec(a),vec(b),andvec(c) be three vectors having magnitudes 1,1,2 respectively. If vec(a)xx(vec(a)xxvec(c))+vec(b)=0, then the acute angle between vec(a)andvec(c) is ……………

If absvec(a)=absvec(b)=1" such that "vec(a)+2vec(b)and5vec(a)-4vec(b) are perpendicular to each other, then the angle between vec(a)andvec(b) is

If vec a , vec b ,a n d vec c are non-zero vectors such that vec adot vec b= vec adot vec c , then find the geometrical relation between the vectors.

Let vec a , vec b , vec c be three unit vectors and vec a . vec b= vec a . vec c=0. If the angel between vec b and vec c is pi/3 , then find the value of |[ vec a vec b vec c]| .