Show that the vectors `hati-3hatj+2hatk, 2hati-4hatj-hatk and 3hati+2hatj-hatk` are linearly independent

Show that the vectors hati-3hati+2hatk,2hati-4hatj-hatk and 3hati+2hatj-hatk and linearly independent.

Show that the vectors 4hati-hatj+hatk, 3hati-2hatj-hatk and hati+hatj+2hatk are co-planar.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

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

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

Find lambda if the vectors hati+hatj+2hatk, lambdahati-hatj+hatk and 3hati-2hatj-hatk are coplanar.

Show that vectors 3hati-2hatj+2hatk,hati-3hatj+4hatk and 2hati-hatj-2hatk form a right angled triangle