Question

The vectors $\mathbf{c},\mathbf{a} = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}$ and $\mathbf{b} = \mathbf{j}$ are such that a,c, b form a right handed system, then c is

• A. $z\mathbf{i} - x\mathbf{k}$
• B. 0
• C. $y\mathbf{j}$
• D. $- z\mathbf{i} + x\mathbf{k}$

Answer 1

Answer: (A)

$z\mathbf{i} - x\mathbf{k}$

Answer 2

Since $\mathbf{a},\mathbf{b},\mathbf{c}$ form a right handed system

$\therefore\mathbf{c} = \mathbf{b} \times \mathbf{a} = \mathbf{j} \times (x\mathbf{i} + y\mathbf{j} + z\mathbf{k})$

$= x(\mathbf{j} \times \mathbf{i}) + z(\mathbf{j} \times \mathbf{k}) = - x\mathbf{k} + z\mathbf{i} = z\mathbf{i} - x\mathbf{k}$.