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.

Find a unit vector in the direction of the resultant of the vectors (hati+2hatj+3hatk),(-hati+2hatj+hatk) and (3hati+hatj) .

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

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

Find the angle between the lines vecr = (hati+hatj)+lambda (hati+hatj+hatk)and vecr=(2hati-hatj)+t(2hati+3hatj+hatk)

The position vector of A,B,C are (hati+2hatj+3hatk),(-2hati+3hatj+5hatk) and ( 7hati-hatk ) respectively. Prove that A,B and C are collinear.

Find a unit vector perpendicular to both the vectors (2hati+3hatj+hatk) and (hati-hatj+2hatk) .

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

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk