If the vectors `(a hat i+2hat j +3 hat k)` and `(3 hat i+b hat j)` are perpendicular then prove that `3a+2b=0`

A vector of magnitude sqrt(2) coplanar with the vecrtor vec a=hat i+hat j+2hat kandvec b=hat i+2hat j+hat k, and perpendicular to the vector vec c=hat i+hat j+hat k is a.-hat j+hat k b.hat i-hat k c.hat i-hat j d.hat i-hat j

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are

The vector(s) which is/are coplanar with vectors hat(i)+hat(j)+2hat(k) and hat(i)+2hat(j)+hat(k) are perpendicular to the vector hat(i)+hat(j)+hat(k) is are

If vectors vec(a) = 3 hat(i) + hat(j) - 2 hat(k) and vec(b) = hat(i) + lambda(j) - 3 hat (k) are perpendicular to each other , find the value of lambda .

Find the angle between the vectors hat i-2hat j+3hat k and 3hat i-2hat j+hat k

Prove that the vectors A = 2 hati - 3 hat 3 j+hat k and B= hat i+hat j + hat k are mutually perpendicular.

Find 'lambda' when the vectors : vec(a)=2hat(i)+lambda hat(j)+hat(k) and vec(b)=hat(i)-2hat(j)+3hat(k) are perpendicular to each other.

If vec P=hat i+hat j+2hat k and vec Q=3hat i-2hat j+hat k ,the unit vector perpendicular to both bar(P) and bar(Q) is (A) (hat i+hat j-hat k)/(sqrt(3)) (B) 5(hat i+hat j-hat k) (C) (1)/(sqrt(3))(hat i-hat j+hat k) (D) (1)/(25)(hat i+hat j-hat k)

Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors 2 hat i +4 hat j-5 hat k and hat i+2 hat j+3 hat k.Then if vec a is a unit vector parallel to AC then = (a) 1/3(3 hat i-6 hat j-2 hat k) (b) 1/3(3 hat i +6 hat j+2 hat k) (c) 1/7(3 hat i +6 hat j+2 hat k) (d) 1/7(3 hat i +6 hat j-2 hat k)

The magnitude of the projection of the vector 2hat i+3hat j+hat k on the vector perpendicular to the plane containing the vectors hat i+hat j+widehat K and hat j+3hat 2j+3hat k is :