Question

Let a = i + j + k, b = i and c = c₁j + c₂j + c₃k. Then, If c₁ = -1 and c₃ = 1, show that no value of c₁ can make vectors a, b and c coplanar.

Answer 1

Formula: -

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

We know that \(\vec a,\,\vec b, \,\vec c \) are coplanar if

⇒ 0 – 1(c₃) + 1(2) = 0

⇒ c₃ = 2