If `vec A=hat i` is rotated by `45^(@)` anticlockwise in x- y plane then new vector formed is:

The vector vec(OA) where O is origin is given by vec(OA) = 2 hati + 2 hatj . Now it is rotated by 45^(@) anticlockwise about O . What will be the new vector . ?

A vector 4hat i+3hat j rotates about its tail through an angle 53^(@) in anticlockwise direction then the new vector is

If |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-a)^2|=0 and vectors vec A , vec B ,a n d vec C , w h e r e vec A=a^2 hat i+a hat j+ hat k , etc, are non-coplanar, then prove that vectors vec X , vec Ya n d vec Z ,w h e r e vec X=x^2 hat i+x hat j+ hat k , etc. may be coplanar.

A non zero vector vec a is parallel to the line of intersection of the plane determined by the vectors hat i,hat i+hat j and the plane determined by by by the vectors hat i-hat j,hat i+hat k. The angle between vec a and hat i-2hat j+2hat k can be

Let vec a=hat i be a vector which makes an angle of 120^(@) with a unit vector vec b in XY plane.then the unit vector (vec a+vec b) is

Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k be three vectors. A vector vec v in the plane of vec aa n d vec b , whose projection on vec c is 1/(sqrt(3)) is given by a. hat i-3 hat j+3 hat k b. -3 hat i-3 hat j+3 hat k c. 3 hat i- hat j+3 hat k d. hat i+3 hat j-3 hat k

vec a=hat i+hat j+hat k,vec b=hat i-hat j+hat k and vec c=hat i-hat j-hat k' be three vectors.A vector vec v in the plane of vec a and vec b. whose projection on vecc is (1)/(sqrt(3)), is given by

The vector vec P=alphahat i+betahat j+gammahat k, alpha!=0 ,lies in the plane of the vector vec Q=hat i+hat j and vec R=hat i+hat k and bisects the angle between vec Q and vec R .Then the value of (3 beta+4 gamma)/(2 alpha) is