Question

Show that each of the following triads of vectors is coplanar : a = i - 2j + 3k, b = -2i + 3j - 4k, c = i - 3j + 5k

Answer 1

Formula:-

(iii) Three vectors  \(\vec a,\,\vec b\) and  \(\vec c\) are coplanar if and only if  \(\vec a.(\vec b\times\vec c)=0\)

Given:-

we know that three vector  \(\vec a,\vec b,\vec c\) are coplanar if their scalar triple product is zero

\([\vec a,\vec b,\vec c]\) = 0.

We have

= 1(15 – 12) + 2( – 10 + 4) + 3(6 – 3)

= 3 – 12 + 9 = 0