Question

If vectors $\overrightarrow{A} = 2\mathbf{i} + 3\mathbf{j} + 4\mathbf{k}$, $\overrightarrow{B} = \mathbf{i} + \mathbf{j} + 5\mathbf{k}$, and $\overrightarrow{C}$ form a left handed system, then $\overrightarrow{C}$ is

• A. 11i – 6j – k
• B. – 11i + 6j + k
• C. 11i – 6j + k
• D. – 11i + 6j – k

Answer 1

Answer: (B)

– 11i + 6j + k

Answer 2

$\overset{\rightarrow}{A} = 2i + 3j + 4k$ and $\overset{\rightarrow}{B} = i + j + 5k$

$\overset{\rightarrow}{A},\overset{\rightarrow}{B}$ and $\overset{\rightarrow}{C}$ form a left or right handed system according as $\lbrack\overset{\rightarrow}{A}\overset{\rightarrow}{B}\overset{\rightarrow}{C}\rbrack < 0$ or $> 0$ respectively.

Here, $\lbrack\overset{\rightarrow}{A}\overset{\rightarrow}{B}\overset{\rightarrow}{C}\rbrack < 0$, ∴ $\overset{\rightarrow}{C} = - 11i + 6j + k.$