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For an arbitrary vector p, what is the value of (3/2) [|p × î|² + |p × ĵ|² + |p × k̂|²] ?

1. p²
2. 2p²
3. 3p²
4. 4p²

Correct answer: 3p²

Solution

|p x i|^2 + |p x j|^2 + |p x k|^2 = (p2^2+p3^2)+(p1^2+p3^2)+(p1^2+p2^2) = 2(p1^2+p2^2+p3^2) = 2p^2. Multiplying by 3/2 gives 3p^2.

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