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Question

The value of |a×^i|2+|a×^j|2+|a×^k|2 is equal to

A
|a|2
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B
2|a|2
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C
3|a|2
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D
6|a|2
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Solution

The correct option is B 2|a|2
a×^i2+a×^j2+a×^k2Leta=(a1^i+a2^j+a3^k)a×^i=∣ ∣ ∣^i^j^ka1a2a3100∣ ∣ ∣=^i(00)^j(0a3)+^k(0a3)=(a3.^ja2^k)a×^j=a3^i+a1^ka×^k=a2^ia1^j=a23+a22+a23+a21+a22+a21=2(a21+a22+a23)=2|a|2Hence,optionBiscorrectanswer.

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