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

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

If vec aa n d vec b are two unit vectors and theta is the angle between them, then the unit vector along the angular bisector of vec a and vec b will be given by a. ( vec a- vec b)/(cos(theta//2)) b. ( vec a+ vec b)/(2cos(theta//2)) c. ( vec a- vec b)/(2cos(theta//2)) d. none of these

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 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

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]| .

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) , vec(b)and vec(a) xx vec(b) are three unit vectors , find the angles beween the vectors vec(a) and vec(b)

If the two adjacent sides of two rectangles are represented by vectors vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec b \ and \ vec r=-4 vec a- vec b ; vec s=- vec a+ vec b , respectively, then the angel between the vector vec x=1/3( vec p+ vec r+ vec s) \ and \ vec y=1/5( vec r+ vec s) is a. -cos^(-1)((19)/(5sqrt(43))) b. cos^(-1)((19)/(5sqrt(43))) c. pi-cos^(-1)((19)/(5sqrt(43))) d. cannot be evaluate

If vec a and vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a and vec b .

vec aa n d vec b are two unit vectors that are mutually perpendicular. A unit vector that is equally inclined to vec a , vec ba n d vec axx vec b is a. 1/(sqrt(2))( vec a+ vec b+ vec axx vec b) b. 1/2( vec axx vec b+ vec a+ vec b) c. 1/(sqrt(3))( vec a+ vec b+ vec axx vec b) d. 1/3( vec a+ vec b+ vec axx vec b)