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

Question

Let $\vec a=3\hat i+\hat j$, $\vec b=\hat i+2\hat j+\hat k$. Let $\vec c$ satisfy $\vec a	imes(\vec b	imes\vec c) = \vec b+\lambda\vec c$. If $\vec b,\vec c$ are non-parallel, the value of $\lambda$ is:

Accepted Answer

$$\vec a\times(\vec b\times\vec c) = (\vec a\cdot\vec c)\vec b - (\vec a\cdot\vec b)\vec c$$

Comparing with $\vec b+\lambda\vec c$ (since $\vec b,\vec c$ are independent, coefficients must match): $\vec a\cdot\vec c=1$ and $-(\vec a\cdot\vec b)=\lambda$.

$$\vec a\cdot\vec b = 3(1)+1(2)+0(1) = 5 \implies \lambda=-5$$

Solutions · 1