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標題:

Vector (What's Wrong?)

發問:

Let a,b be 2 vectors.|a?b|=||a||b|cosθ|

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最佳解答:

Let a, b be 2 vectors. |a?b| =|a||b|cosθ| ∵ 1≥|cosθ|≥0 |a||b|≥|a||b||cosθ|≥|a||b|X0 ∴ |a||b|≥|a||b||cosθ|≥0 |a?b|≤|a||b| 2012-07-07 00:01:16 補充： So WHAT'S WRONG with your process? ∵ |cosθ| ≥ 0 correct ∴ |a| |b| |cosθ| ≥ |a| |b| WRONG ! ∵ |cosθ| ≥ 0 Both sides multiplied by |a||b|, we have ( |a| |b| ) |cosθ| ≥ ( |a| |b| ) X 0 ∴ |a| |b| |cosθ| ≥ 0 2012-07-07 00:02:06 補充： If |a| |b| |cosθ| ≥ |a| |b| Then |cosθ| ≥ 1 which is impossible In fact, 1 ≥ |cosθ| Both sides multiplied by |a| |b|, we have |a| |b| ≥ |a| |b| |cosθ|

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