The unit vector perpendicular to both the vectors i -2j + 3k and … - Vidyadip

MCQ

The unit vector perpendicular to both the vectors $i -2j + 3k$ and $i + 2j -k$ is

✓
$\frac{1}{{\sqrt 3 }}( - i + j + k)$
B
$( - i + j + k)$
C
$\frac{(i+j-k)}{\sqrt{3}}$
D
None of these

✓

Answer

Correct option: A.

$\frac{1}{{\sqrt 3 }}( - i + j + k)$

a
(a) Unit vector=$=\frac{(i-2j+3k)\times (i+2j-k)}{|(i-2j+3k)\,\times (i+2j-k)|}=\frac{-\,i+j+k}{\sqrt{3}}.$

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