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+4hatk

Find the angle between the following pairs of vectors 3hati+2hatj-6hatk, 4hati-3hatj+hatk , hati-2hatj+3hatk, 3hati-2hatj+hatk

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

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 right 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 four points 6 hati - 7hatj, 16hati - 19 hatj - 4hatk, 3hatj - 6hatk and 2hati + 5hatj + 10 hatk form a tetrahedron in spacel.

Find the angle between the following vectors : (i) veca = 2hati-6hatj+3hatk and vecb = hati+2hatj-2hatk (ii) veca=6hati+3hatj-2hatk and vecb=4hati-2hatj+9hatk