Question

Let $\overset{\rightarrow}{A} = i + j + k$, $\overset{\rightarrow}{B} = i,\overset{\rightarrow}{C} = C_{1}i + C_{2}j + C_{3}k$. If $C_{2} = - 1$, and $C_{3} = 1$, then to make three vectors coplanar

• A. $C_{1} = 0$
• B. $C_{1} = 1$
• C. $C_{1} = 2$
• D. No value of $C_{1}$ can be found

Answer 1

Answer: (D)

No value of $C_{1}$ can be found

Answer 2

To make three vectors coplanar $\lbrack\overset{\rightarrow}{A}\overset{\rightarrow}{B}\overset{\rightarrow}{C}\rbrack = 0$

The value of $\lbrack\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}\rbrack$ is independent of $C_{1}$,

hence no value of $C_{1}$ can be found.