If ` vec aa n d vec b` are two unit vectors incline at angle `pi//3` , then `{ vec axx( vec b+ vec axx vec b)}dot vec b` is equal to `(-3)/4` b. `1/4` c. `3/4` d. `1/2`

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 vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 , then find the angle between vec ba n d vec b- vec adot

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If vec aa n d vec b are any two unit vectors, then find the greatest positive integer in the range of (3| vec a+ vec b|)/2+2| vec a- vec b| .

If vec a and vec b are two vectors, then prove that ( vec axx vec b)^2=|[vec a.vec a,vec a.vec b],[vec b.vec a,vec b.vec b]| .

Let vec aa n d vec b be unit vectors that are perpendicular to each other. Then [ vec a+( vec axx vec b) vec b+( vec axx vec b) vec axx vec b] will always be equal to 1 b. 0 c. -1 d. none of these

If vec ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot

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 aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=sqrt3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ vec b .