If the angel between unit vectors ` vec aa n d vec b60^0` , then find the value of `| vec a- vec b|dot`

If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a- vec b|dot

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]| .

If vec a , vec b ,a n d vec c are there mutually perpendicular unit vectors and vec d is a unit vector which makes equal angles with vec a , vec b ,a n d vec c , the find the value off | vec a+ vec b+ vec c+ vec d|^2dot

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

Let vec aa n d vec b be unit vectors such that | vec a+ vec b|=sqrt(3) . Then find the value of (2 vec a+5 vec b)dot(3 vec a+ vec b+ vec axx vec b)dot

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 .

If vec a , vec ba n d vec c are three non-zero vectors, no two of which ar collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c|dot

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

If theta is th angel between the unit vectors a and b , then prove that cos(theta/2)=1/2| vec a+ vec b| .,, sin(theta/2)=1/2| vec a- vec b|

If ( vec axx vec b)^2+( vec a dot vec b)^2=144a n d| vec a|=4, then find the value of | vec b|dot