If with reference to the right handed system of mutually perpendicular unit vectors `hati,hatjandhatk,,vecalpha=3hati-hatj,vecbeta=2hati+hatj-3hatk`, then express `vecbeta` in the form `vecbeta=vecbeta_(1)+vecbeta_(2)` , where `vecbeta_(1)` is parallel to `vecalphaandvecbeta_(2)` is perpendicular to `vecalpha`.

If with reference to the right handed system of mutually perpendicular unit vectors hati,hatj and 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) .

Find lambda if the vectors hati-hatj+hatk, 3hati-hatj+2hatk and hati+lambda hatj-3hatk are coplannar.

if three vectors are veca=-3hati+2hatj-hatk, vecb=hati-3hatj+5hatk and vecc=2hati+hatj-4hatk then find a-b-c is

Find a vector perpendicular to both the vectors hati-2hatj+3hatk and hati+2hatj-hatk .

If the vectors hati-hatj+hatk,3hati+hatj+2hatk and hati+lambda hatj-3hatk are coplanar then find the value of lambda .

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

A vector perpendicular to (4hati-3hatj) may be :

Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5hatkandvecc=hati-6hatj--7hatk .

If the vectors 2hati-hatj+hatk,hati+2hatj-3hatk and 3hati+ahatj+5hatk are coplanar, the prove that a=-4.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati-2hatj-4hatk are coplanar.