The vector `veca=alpha hati+2hatj+betahatk` lies in the plane of vectors `vecb=hati+hatj and vecc=hatj+hatk` and bisects the angle between `vecb and vecc`. Then which one of the following gives possible values o `alpha and beta?` (A) `alpha=2, beta=1` (B) `alpha=1, beta=1` (C) `alpha=2, beta=1` (D) `alpha=1, beta=2`

The vector vec a=""alpha hat i+2 hat j+""beta hat k lies in the plane of the vectors vec b="" hat"i"+ hat j and vec c= hat j+ hat k and bisects the angle between vec b and vec c . Then which one of the following gives possible values of alpha"and"beta ? (1) alpha=""2,beta=""2 (2) alpha=""1,beta=""2 (3) alpha=""2,beta=""1 (4) alpha=""1,beta=""1

Let A vector veca =alpha hati + 2hatj + beta hatk (alpha, beta in R) , veca lies in the plane of the vectors, vecb= hati + hatj and vecc= hati -hatj+4hatk . If veca bisects the angle between vecb and vecc , then :

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) then tan(alpha+2 beta)tan(2 alpha+beta)=

If veca=hati+hatj+hatk, hatb4hati+3hatj+4hatk and vecc=hati+alphahatj+beta hatk are linearly dependent vectors and |vecc|=sqrt(3) then (A) alpha=1, beta=-1 (B) alpha=1,beta=+-1 (C) alpha-1,beta=+-1 (D) alpha=+-1,beta=1

Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk and vecc= hati+hatj-hatk A vector in the plane of veca and vecb whose projections on vecc is 1//sqrt3 is

If sin (alpha + beta)=1, sin (alpha- beta)= (1)/(2) , then tan (alpha + 2beta) tan (2alpha + beta) =