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

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

Prove that the vectgors 2hati-hatj+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk form a righat angled triangle.

Prove that the points hati-hatj, 4hati-3hatj+ hatk and 2hati-4hatj+5hatk are the vertices of a righat angled triangle.

Find the angel between the following pairs of vectors 2hati-3hatj+hatk, 3hati-hatj-2hatk

Prove that the vecotos 3hati+5hatj+2hatk, 2hati-3hatj-5hatk and 5hati+2hatj-3hatk form the sides of an equlateral triangle.

Using dot product of vectors show that the vectors 2hati-hatj+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk form a righat angled triangle

Prove that the points 2hati-hatj+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk are the vertices of a righat angled triangle. Also find the remaining angles of the triangle.