Prove that:` (2hati+3hatj)xx(hati+2hatj)=hatk`

Find the value of |(hati+hatj)xx(hati+2hatj+hatk)|

Prove that points hati+2hatj-3hatk, 2hati-hatj+hatk and 2hati+5hatj-hatk form a triangle in space.

Prove that the plane vecr*(hati+2hatj-hatk)=3 contains the line vecr=hati+hatj+lamda(2hati+hatj+4hatk).

If the lines hati-(hati+hatj+hatk) xx (1-p)hati+3hatj-2hatk=0 and (vecc-(3hati+hatj-5hatk)) xx (1-p)hati+3hatj-2hatk=0 are coplanar then the value of p is

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