Let a, b, c satisfy a= b( b c), with | a|=√2,| b|=1,| c|=2, and angle (0,2) between b, c.

Question

Accepted Answer

$\vec a = (\vec b\cdot\vec c)\vec b-(\vec b\cdot\vec b)\vec c = 2\cos\theta\,\vec b-\vec c$ (using $|\vec b|=1$).

$$|\vec a|^2 = 4\cos^2\theta+4-2(2\cos\theta)(\vec b\cdot\vec c) = 4\cos^2\theta+4-8\cos^2\theta = 4-4\cos^2\theta = 2$$
$$\cos^2\theta = \frac12 \implies \theta=\frac\pi4 \implies \tan\theta=1$$

$$1+\tan\theta = 2$$

Solutions · 1