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

Question

Let $\vec a=3\hat i+2\hat j+2\hat k$, $\vec b=\hat i+2\hat j-2\hat k$. A vector perpendicular to both $\vec a+\vec b$ and $\vec a-\vec b$ with magnitude 12 is:

Accepted Answer

$\vec a+\vec b=4\hat i+4\hat j$, $\vec a-\vec b=2\hat i+4\hat k$.

$$(\vec a+\vec b)\times(\vec a-\vec b) = \begin{vmatrix}\hat i&\hat j&\hat k\4&4&0\2&0&4\end{vmatrix} = 16\hat i-16\hat j-8\hat k = 8(2\hat i-2\hat j-\hat k)$$

A vector of magnitude 12 along this direction: $12\cdot\dfrac{(2,-2,-1)}{3} = 4(2\hat i-2\hat j-\hat k)$.

*(The listed option B shows coefficient $-2$ for $\hat k$ rather than the derived $-1$ --- likely a minor OCR slip in the source's answer choices; the direction and the answer letter B are retained as given.)*

Solutions · 1