If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three vectors such that $\mathbf{a} \times…

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three vectors such that $\mathbf{a} \times \mathbf{b}=\mathbf{c}, \mathbf{b} \times \mathbf{c}=\mathbf{a}$ and $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are mutually perpendicular to each other, then $|\mathbf{b}|$ is equal to
  1. -1 only
  2. 0 only
  3. 1 only
  4. $\pm 1$

Solution

It is given that $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are mutually perpendicular vectors, such that $\mathbf{a} \times \mathbf{b}=\mathbf{c}$ and $\mathbf{b} \times \mathbf{c}=\mathbf{a}$. So, $ (b \times c) \times b=c $ $\Rightarrow$ (b b) $\mathbf{c}-(\mathbf{b} \cdot \mathbf{c}) \mathbf{b}=\mathbf{c}$ $\Rightarrow \quad \mathbf{b} \cdot \mathbf{b}=\mathbf{l} \Rightarrow|\mathbf{b}|^2=\mathbf{l} \Rightarrow|\mathbf{b}|=\mathbf{l}$

Asked in: AP EAMCET 2020 (22 Sep Shift 1)

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