Question

Show that each of the following triads of vectors is coplanar : a = -4i - 6j - 2k, b = -i + 4j + 3k, c = -8i - j + 3k

Answer 1

Formula : -

(iii) Three vectors  \(\vec a,\,\vec b\) \(\vec c\) are coplanar if their scalar triple product is zero

\([\vec a,\vec b,\vec c]\) = 0.

We have

= – 4(12 + 13) + 6( – 3 + 24) – 2(1 + 32)

= 0

Hence, the Given vector are coplanar.