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`

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

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

Let veca = hatj - hatk and vecc = hati - hatj - hatk. Then the vector vecb satisfying veca xx vecb + vecc= vec0 and veca. Vecb=3 is :

Let veca = hati- hatk, vecb = x hati + hatj + (1-x) hatk and vec c = y hati + x hatj + (1+ x -y) hatk. Then [veca vecb vec c] depends on:

If veca = ahti - ahtk, vecb = x hati + hatj + (1-x) hatk and vecc = y hati + x hatj + 1(+ x -y) hatk, then [veca vecb vecc] depends on :

The vector veca = hati + hatj + (m + 1) hatk , vecb = hati + hatj + m hatk.vecc = hati - hatj + m hatk are coplanar for :

If a=hati+2hatj+3hatk,b=-hati+2hatj+hatk and c=3hati+hatj , then the unit vector along its resultant is

Statement 1 : Let A(veca), B(vecb) and C(vecc) be three points such that veca = 2hati +hatk , veb = 3hati -hatj +3hatk and vecc =-hati +7hatj -5hatk . Then OABC is tetrahedron. Statement 2 : Let A(veca) , B(vecb) and C(vecc) be three points such that vectors veca, vecb and vecc are non-coplanar. Then OABC is a tetrahedron, where O is the origin.