If `vecalpha=3hati+4hatj+5hatk` and `vecbeta=2hati+hatj-4hatk`, then express `vecbeta` in the form `vecbeta=vec(beta_1)+vec(beta_2)`, where `vec(beta_1)` is parallel to `vecalpha` and `vec(beta_2)` is perpendicular to `vecalpha`.

If with reference to the right handed system of mutually perpendicular unit vectors hati, hatj, hatk , vec alpha = 3hati - hatj, vec beta = 2hati + hatj - 3hatk , then express vec beta in the form vec beta = vec beta_1 + vec beta_2 where vec beta_1 is parallel to vec alpha and vec beta_2 is perpendicular to vec alpha .

If vec alpha=3 hat i-hat j and beta=2 hat i+hat j-3 hat k , express vec beta in the form vec beta=vec (beta)_1+ vec (beta)_2 where beta_1 is parallel to vec alpha and vec(beta)_2 is perpendicular to vec alpha .

If vec a=2hati+3hatj-hatk , then |vec a| is :

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

If vec(OP)=2hati+3hatj-hatk and vec(OQ)=3hati-4hatj+2hatk find the modulus and direction cosines of vec(PQ) .

If veca=5hati+hatj-4hatk, vecb=2hati-3hatj+hatk and vecc=hati+3hatj-2hatk then find a unit vector parallel to the vector 2veca+vecb+3vecc .