Question

Show that the following vectors are coplanar.

(i) i - 2j + 3k, -2i + 3j - 4k, - j + 2k 

(ii) 2i + 3j + k, i - j, 7i + 3j + 2k 

Answer 1

Let the given three vectors be vector a, b and c. When we are able to write one vector as a linear combination of the other two vectors, then the given vectors are called coplanar vectors.

(i) Let vector a = m vector b + n vector c where

(i.e.) vector a =  i - 2j + 3k

n = 1/2

∴ We are able to write one vector as a linear combination of the other two 

The given vectors are coplanar.

(ii) Let the given vectors be a, b and c.

Let 

We are able to write vector a as a linear combination of vector (b and c)

∴ The vectors (a, b, c) are coplanar