Let a=3 i+2 j+x k, b= i- j+ k.

Question

Let $\vec a=3\hat i+2\hat j+x\hat k$, $\vec b=\hat i-\hat j+\hat k$. Then $|\vec a	imes\vec b|=r$ is possible if:

Accepted Answer

$$\vec a\times\vec b = \big((2+x),\ (x-3),\ -5\big)$$
$$r^2 = (2+x)^2+(x-3)^2+25 = 2x^2-2x+38 = 2\left(x-\frac12\right)^2+\frac{75}2$$

Minimum value $\dfrac{75}2$ occurs at $x=\dfrac12$, so $r\ge\sqrt{\dfrac{75}2}=\dfrac{5\sqrt6}2$.

Solutions · 1