If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are non-zero vectors such $\mathbf{a} \times…

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are non-zero vectors such $\mathbf{a} \times \mathbf{b}=\mathbf{c}$ and $\mathbf{b} \times \mathbf{c}=\mathbf{a}$, then $\mathbf{a} \times \mathbf{c}$ is
  1. equal to $\mathbf{b}$
  2. parallel to $\mathbf{b}$
  3. perpendicular to $\mathbf{b}$
  4. parallel to $\mathbf{a}$

Solution

Given, $\mathbf{a} \times \mathbf{b}=\mathbf{c}$ and $\mathbf{b} \times \mathbf{c}=\mathbf{a}$ Here, $a, b, c$ are mutually perpendicular vectors. $\therefore \mathbf{a} \times \mathbf{c}$ is parallel to $\mathbf{b}$.

Asked in: AP EAMCET 2021 (25 Aug Shift 1)

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