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If $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$ and $|\mathbf{a}|=3$, then $|\mathbf{a}|$ is equal to
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The correct answer is:
2
Given, $|\mathbf{a} \times \mathbf{b}|+|\mathbf{a} \cdot \mathbf{b}|^2=36$ and $|\mathbf{a}|=3$
Correct one is $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$ and $|\mathbf{a}|=3$
We know, $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=|\mathbf{a}|^2|\mathbf{b}|^2$
$$
\begin{array}{ll}
\therefore & |\mathbf{a}|^2|\mathbf{b}|^2=36 \Rightarrow(3)^2|\mathbf{b}|^2=36 \\
\Rightarrow & |b|^2=4 \Rightarrow|b|=2
\end{array}
$$
Hence, the correct option is (4).
Correct one is $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$ and $|\mathbf{a}|=3$
We know, $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=|\mathbf{a}|^2|\mathbf{b}|^2$
$$
\begin{array}{ll}
\therefore & |\mathbf{a}|^2|\mathbf{b}|^2=36 \Rightarrow(3)^2|\mathbf{b}|^2=36 \\
\Rightarrow & |b|^2=4 \Rightarrow|b|=2
\end{array}
$$
Hence, the correct option is (4).
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