Question

Show that the points A( – 1, 4, – 3), B(3, 2, – 5), C( – 3, 8, – 5) and D( – 3, 2, 1) are coplanar.

Answer 1

Formula: -

Given: -

AB = position vector of B - position vector of A

= \(4\hat i-2\hat j-2\hat k\)

AC = position vector of C - position vector of A

 = \(-2\hat i+4\hat j-2\hat k\)

AD = position vector of C - position vector of A

= \(-2\hat i-2\hat j+2\hat k\)

The four pint are coplanar if the vector are coplanar.

thus,

= 4(16 - 4) + 2( - 8 - 4) - 2( - 4 + 8) = 0

Hence proved.