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| .

A = vec(i) + vec(j) . What is the angle between the vector and x-axis ?

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

Vector vec a , vec b and vec c are such that vec a+ vec b+ vec c= vec0 and |a|=3,| vec b|=5 and | vec c|=7. Find the angle between vec a and vec b .

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

Which of the following is/are correct? (a)If vec a= hat i+ hat j and vec b=2 hat i- hat k then the point of intersection of the lines vec r x vec a = vec b x vec a and vec a x vec b = vec a x vec b is 3 vec i + vec j - veck (b)( vec r dot hat i )( hat i x vec r )+( vec r dot hat j )( hat j x vec r )+( vec r dot hat k )( hat k x vec r )= vec0 (c)If | vec a|=3,| vec b|=5,| vec c|=7 and vec a+ vec b+ vec c= vec0 then the angle between vec aa n d vec b is pi/3 (d)If the vectors vec a , vec b& vec c from the sides B C ,C A&A B respectively of a triangle A B C , then vec a x vec b = vec b x vec c x vec a

If vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is pi/2, then

If vec a and vec b are two vectors such that | vec a|=4,| vec b|=3 and vec a . vec b=6 . Find the angle between vec a 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 .