Find a unit vector `vec c` if `vec -i+vec j-vec k` bisects the angle between `vec c and 3 vec i+4vec j`.

If vector vec a+ vec b bisects the angle between vec a and vec b , then prove that | vec a| = | vec b| .

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]| .

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=

If vec a and vec b be two unit vectors such that vec a+ vec b is also a unit vector, then find the angle between vec a and vec b

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

Find lambda if the vectors vec a= vec i+3 vec j+ vec k , vec b= 2 vec i- vec j- vec k and vec c= lambda vec i+7 vec j+ 3 vec k are coplanar

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot

(i) If vec a, vec b and vec a + vec b are unit vectors, then prove that the angle between vec a and vec b is (2pi)/(3) (ii) If (2 hat i + hat j - 3 hat k ) and (m hat i + 3 hat j - hat k) are perpendicular to each other , then find m.

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .

Consider the vectors veca = hat i + 3 hat j + hat k and vec b = 2 hat i - hat j - hat k . (i) Find vec a.vec b (ii) Find the angle between vec a and vec b .