Find the values of x for which `x(hati+hatj+hatk)` is a unit vector

Find the value of a for which the vectors 3 hati + 3hatj + 9 hatk and hati + a hatj +3 hatk are parallel.

Find the value of m so that the vector 3 hati - 2hatj +hatk is perpendicular to the vector. 2hati +6hatj +m hatk .

Find the value of p, if the vectors hati - 2hatj + hatk , 2hati - 5hatj + phatk and 5hati - 9hatj + 4hatk are coplanar .

The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is

A vector vec P when added to the sum of the vectors 2hati-3hatj+hatk and -3hati-hatj+hatk gives a unit vector along the x-axis. What is the magnitude of the vector vec P ?

Find the projection of vector veca=5hati-hatj-3hatk on the vector vecb=hati+hatj+hatk .

Find the projection of the vector hati-2hatj+hatk on the vector 4hati-4hatj+7hatk .

The unit vector which is orthogonal to the vector 5hatj + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is