Prove th the following sets of three points are collinear: `2hati+hatj-hatk, 3hati-2hatj+hatk and hati+4hatj-3hatk`

Prove that the following vectors are at righat angle: 2hati+5hatj+hatk, 3hati-2hatj+hatk

The position vectors of the points A,B and C are (2hati + hatj - hatk), (3hati - 2hatj + hatk) and (hati + 4hatj - 3hatk) respectively. Show that the points A,B and C are collinear.

If the position vectors of the three points A,B,C are 2hati+4hatj-hatk, hati+2hatj-3hatk and 3hati+hatj+2hatk respectively, find a vector perpendicular to the plane ABC.

Three vectors 7hati-11hatj+hatk, 5hati+3hatj-2hatk and 12hati-8hatj-hatk forms

Prove that the following vectors are at righat angle: 2hati-hatj+hatk ,hati-3hatj+5hatk

Prove that the three points whose positions vectors are 3hati-hatj+2hatk, hati-hatj-3hatk and 4hai-3hatj+hatk form an isosceles tirangle.

The points with position vectors 5hati + 5hatk, -4hati + 3hatj - hatk and 2hati +hatj + 3hatk

Find the scalar triple product vectors hati+2hatj+3hatk, hati-hatj+hatk and hati+hatj+hatk .

Find the scalar triple product of vectors hati+2hatj+3hatk, -hati-hatj+hatk and hati+hatj+hatk .