Let the vectors `veca,vecbvecc` be given as `a_(1)hati+a_(2)hatj+a_(3)hatk,b_(1)hati+b_(2)hatj+b_(3)hatkc_(1)hati+c_(2)hatj+c_(3)hatk`. Then show that `vecaxx(vecb+vecc)=vecaxxvecb+vecaxxvecc`

vec(a)=hati-2hatj+hatk,vec(b)=2hati+hatj+hatk , vec( c )=hati+2hatj-hatk then find that vec(a)xx(vec(b)xxvec( c )) .

bar(a)=a_(1)hati+a_(2)hatj+a_(3)hatk,bar(b)=b_(1)hati+b_(2)hatj+b_(3)hatk,bar( c )=c_(1)hati+c_(2)hatj+c_(3)hatk are three non zero vectors. The unit vector bar( c ) is perpendicular to bar(a) and bar(b) . The angle between bar(a) and bar(b) is (pi)/(6) then, |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| = .............

Find [vec(a)vec(b)vec( c )] if vec(a)=hati-2hatj+3hatk,vec(b)=2hati-3hatj+hatk and vec( c )=3hati+hatj-2hatk .

If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+hatj+2hatk then find vec(a).(vec(b)xx vec( c )) .

vec(a)=2hati-10hatj+2hatk,vec(b)=3hati+hatj+2hatk and vec( c )=2hati+hatj+3hatk then find vec(a)xx(vec(b)xxvec( c )) .

If veca=5hati-hatj-3hatkandvecb=hati+3hatj-5hatk , then show that the vectors veca+vecbandveca-vecb are perpendicular.

If vec(a)=hati+2hatj-3hatk and vec(b)=3hati-hatj+2hatk then show that (vec(a)+vec(b)) is a perpendicular to the vector vec(a)-vec(b) .

vec(a)=2hati-2hatj+hatk,vec(b)=hati+2hatj-2hatk and vec( c )=2hati-hatj+4hatk then find the projection of vec(b)+vec( c ) on vec(a) .

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

Calculate vecr=veca-vecb+vecc where veca=5hati+4hatj-6hatk, vecb=-2hati+2hatj+3hatk and vecc=4hati+3hatj+2hatk .