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Explain why an acute-angle projection has positive sign

Relative to O, A,B have position vectors a,b and c is the position vector of C on AB dividing AB in the ratio 3:1. Given angle AOB is acute, show that the length d of the projection of OC onto OB is d=34∣b∣+a⋅b4∣b∣d=\frac34|\mathbf b|+\frac{\mathbf a\cdot\mathbf b}{4|\mathbf b|}.

CJC · Review problems · Question 13

Use the acute-angle condition to determine the sign before removing absolute values.

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