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Geometric Progression

For any vecto...

Question

For any vector $\to a$ , the value of $(\to a \times^i)^{2} + (\to a \times^j)^{2} + (\to a \times^k)^{2}$ is equal to

A

3 {\to a}^{2}

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B

{\to a}^{2}

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C

2 {\to a}^{2}

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D

4 {\to a}^{2}

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Solution

The correct option is C $2 {\to a}^{2}$
Let $\to a = x^i + y^j + z^k$
$\Rightarrow \to a \times^i = z^j - y^k$
$=> (\to a \times^i)^{2} = y^{2} + z^{2}$
Similarly $(\to a \times^j)^{2} = x^{2} + z^{2}$
and $(\to a \times^k)^{2} = x^{2} + y^{2}$
$∴ (\to a \times^i)^{2} + (\to a \times {^j}^{2} + (\to a \times^k)^{2} = 2 (x^{2} + y^{2} + z^{2}) = 2 {\to a}^{2}$

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Similar questions

{\to A}_{1}

{\to A}_{2}

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