Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
2098 Upvotes
Verified Answer
The correct answer is:
1 only
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) $\mathbf{c}-(\mathbf{b} \cdot \mathbf{c}) \mathbf{b}=\mathbf{c}$
$\Rightarrow \quad \mathbf{b} \cdot \mathbf{b}=\mathbf{l} \Rightarrow|\mathbf{b}|^2=\mathbf{l} \Rightarrow|\mathbf{b}|=\mathbf{l}$
So,
$$
(b \times c) \times b=c
$$
$\Rightarrow$
(b b) $\mathbf{c}-(\mathbf{b} \cdot \mathbf{c}) \mathbf{b}=\mathbf{c}$
$\Rightarrow \quad \mathbf{b} \cdot \mathbf{b}=\mathbf{l} \Rightarrow|\mathbf{b}|^2=\mathbf{l} \Rightarrow|\mathbf{b}|=\mathbf{l}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.