Show that the three points with position vectors `hati+2hatj+7hatk`,`2hati+6hatj+3hatk` and `3hati+10hatj-hatk` are collinear.

Show that the three points with position vectors 2hati+6hatj+3hatk , hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.

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

Show that the points with position vectors veca=3hati-4hatj-4hatk,vecb=2hati-hatj+hatk and vecc=hati-3hatj-5hatk respectively form the vertices of a right angled triangle.

Show that the four points with position vectors 4hati+8hatj+12hatk,2hati+4hatj+6hatk,3hati+5hatj+4hatk and 5hati+8hatj+5hatk are coplanar.

Using vector method, show that the points whose position vectors are , 2hati-hatj+hatk and hati-3hatj-5hatk and 3hati-4hatj-4hatk form a right angled triangle.

Using scalar triple product, show that the four points given by position vectors : 2hati+3hatj+2hatk,4hati-5hatk,3hati+hatj-2hatk and 5hati+3hatj-4hatk are coplanar.

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

Find 'lambda' so that the four points with position vectors -hati+3hatj+2hatk,3hati+lambda hatj+4hatk,5hati+7hatj+3hatk and -13hati+17hatj-hatk are coplanar.

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