Let a, b, c satisfy | a|=√3, | b|=5, b c=10, angle between b, c is 3, and a( b c).

Question

Answer: 30

Accepted Answer

$\vec b\cdot\vec c = |\vec b||\vec c|\cos\dfrac\pi3 = 10 \Rightarrow 5|\vec c|\left(\dfrac12\right)=10 \Rightarrow |\vec c|=4$.

$$|\vec a\times(\vec b\times\vec c)| = |\vec a||\vec b\times\vec c|\sin90^{\circ} = \sqrt3\cdot|\vec b||\vec c|\sin\frac\pi3 = \sqrt3\cdot5\cdot4\cdot\frac{\sqrt3}2 = 30$$

Solutions · 1