For any vector a- the value of a- 2- a- 2- a-k- 2 is equal to

The correct option is D 2|a⃗|^2 Let a̅=a_1î+b_1ĵ+c_1k̂ nbsp; ∴a̅^2=a_1^2+b_1^2+c_1^2 ∴a̅× nbsp;i̅= b_1k̂+c_1ĵ ∴ (a̅×î)^2=b_1^2+c_ ...

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Byju's Answer

Standard XII

Mathematics

Global Maxima

For any vecto...

Question

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

| \to a |^{2}

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3 | \to a |^{2}

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4 | \to a |^{2}

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2 | \to a |^{2}

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Solution

The correct option is D $2 | \to a |^{2}$
Let $¯ a = a_{1}^i + b_{1}^j + c_{1}^k$
$∴ {¯ a}^{2} = a_{1}^{2} + b_{1}^{2} + c_{1}^{2}$ $∴ ¯ a \times ¯ i = - b_{1}^k + c_{1}^j$
$∴ (¯ a \times^i)^{2} = b_{1}^{2} + c_{1}^{2}$
Similarly $(¯ a \times^j)^{2} = a_{1}^{2} + c_{1}^{2}$
$(¯ a \times^k)^{2} = a_{1}^{2} + b_{1}^{2}$
$∴ (¯ a \times^i)^{2} + (¯ a \times^j)^{2} + (¯ a \times^k)^{2} = 2 (a_{1}^{2} + b_{1}^{2} + c_{1}^{2}) = 2 {¯ a}^{2}$

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For any vector ¯a, the value of (¯a×^i)2+(¯a×^j)2+(¯a×^k)2 is equal to

The correct option is D 2|→a|2Let ¯a=a1^i+b1^j+c1^k ∴¯a2=a21+b21+c21 ∴¯a×¯i=−b1^k+c1^j∴(¯a×^i)2=b21+c21 Similarly (¯a×^j)2=a21+c21 (¯a×^k)2=a21+b21 ∴(¯a×^i)2+(¯a×^j)2+(¯a×^k)2=2(a21+b21+c21)=2¯a2

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