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| .

If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

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

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

If vec a , vec b and vec c are non-coplanar unit vectors such that vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2)) , then the angle between vec a and vec b is a. 3pi//4 b. pi//4 c. pi//2 d. pi

If vec a,vec b, vec c be three vectors such that vec a+vec b+vec c=0 , |veca|=3 , |vecb|=5 and |vecc|=7 find the angle between the vectors veca and vec b .

Find a unit vector perpendicular to each of the vectors ( vec a+ vec b) and ( vec a- vec b) , where vec a= hat i+ hat j+ hat k , vec b= hat i+2 hat j+3 hat k .

If vec a=7 hat i-4 hat j-4 hat k and vec b=-2 hat i- hat j+2 hat k , determine vector vec c along the internal bisector of the angle between of the angle between vectors vec a and vec b such that | vec c| =5sqrt(6)

Let vec a= hat i+ hat j ; vec b=2 hat i- hat kdot Then vector vec r satisfying vec rxx vec a= vec bxx vec a and vec rxx vec b= vec axx vec b then vecr is a. hat i- hat j+ hat k b. 3 hat i- hat j+ hat k c. 3 hat i+ hat j- hat k d. hat i- hat j- hat k