Let a = 3 i + 2 j + 2 k and b = i + 2 j - 2 k be two vectors. If … - Vidyadip

MCQ

Let $\vec a = 3\hat i + 2\hat j + 2\hat k$ and $\vec b = \hat i + 2\hat j - 2\hat k$ be two vectors. If a vector perpendicular to both the vectors $\vec a + \vec b$ and $\vec a - \vec b$ has the magnitude $12$ then one such vector is

✓
$4\,\left( {2\hat i - 2\hat j - \hat k} \right)$
B
$4\,\left( {2\hat i - 2\hat j + \hat k} \right)$
C
$4\,\left( {2\hat i + 2\hat j + \hat k} \right)$
D
$4\,\left( {2\hat i + 2\hat j - \hat k} \right)$

✓

Answer

Correct option: A.

$4\,\left( {2\hat i - 2\hat j - \hat k} \right)$

a
$(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})$

$ = 2\left| {\begin{array}{*{20}{c}}
{\hat i}&{\hat j}&{\hat k}\\
1&2&{ - 2}\\
3&2&2
\end{array}} \right|$

$=2(8 \hat{i}-8 \hat{j}+4 \hat{k})$

$\text { Required vector }=\pm 12 \frac{(2 \hat{i}-2 \hat{j}-\hat{k})}{3}$

$=\pm 4(2 \tilde{i}-2 \hat{j}-\hat{k})$

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