vecctor `vec(OA)=hati+2hatj+2hatk` turns through a right angle passing through the positive x-axis on the way. Show that the vector in its new postion is `(4hati-hatj-hatk)/sqrt2`

The position vector of a point at a distance of 3sqrt(11) units from hati-hatj+2hatk on a line passing through the points hati-hatj+2hatk and parallel to the vector 3hati+hatj+hatk is

Find the equation of a line passes through the points whose position vectors are (hati+4hatj+hatk) and (2hati-hatj+5hatk) .

Find the angle between the vectors 4hati-2hatj+4hatk and 3hati-6hatj-2hatk.

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

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

Find the equation of the plane through the point (3,4,-5) and parallel to the vectors 3hati+hatj-hatk and hati-2hatj+hatk .

A unit vector perpendicular to the plane passing through the points whose position vectors are hati-hatj+2hatk, 2hati-hatk and 2hati+hatk is

Equation of a plane passing through the intersection of the planes vecr.(3hati-hatj+hatk)=1 and vecr.(hati+4hatj-2hatk)=2 and passing through the point (hati+2hatj-hatk) is :

The vector equation of a plane passing through a point having position vector 2hati+3hatj-4hatk and perpendicular to the vector 2hati-hatj+2hatk , is

Show that the vectors 2hati-hatj+hatk and hati-3hatj-5hatk are at righat angles.