If a =2 i -3 j - k and b = i +4 j -2 k , then a b is: - Vidyadip

MCQ

If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}},$ then $\vec{\text{a}}\times\vec{\text{b}}$ is:

A
$10\hat{\text{i}}+2\hat{\text{j}}+11\hat{\text{k}}$
✓
$10\hat{\text{i}}+3\hat{\text{j}}+11\hat{\text{k}}$
C
$10\hat{\text{i}}-3\hat{\text{j}}+11\hat{\text{k}}$
D
$10\hat{\text{i}}-2\hat{\text{j}}-10\hat{\text{k}}$

✓

Answer

Correct option: B.

$10\hat{\text{i}}+3\hat{\text{j}}+11\hat{\text{k}}$

$\vec{\text{a}}\times\vec{\text{b}}=\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}}\\2&-3&-1\\1&4&-2 \end{vmatrix}$
$=10\hat{\text{i}}+3\hat{\text{j}}+11\hat{\text{k}}$

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