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

MCQ

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

A
$\frac{-2i+3j+5k}{\sqrt{30}}$
B
$\frac{{ - 2i + 5j + 6k}}{{\sqrt {38} }}$
✓
$\frac{{ - 2i + 3j + 5k}}{{\sqrt {38} }}$
D
$\frac{-2i+4j+5k}{\sqrt{38}}$

✓

Answer

Correct option: C.

$\frac{{ - 2i + 3j + 5k}}{{\sqrt {38} }}$

c
(c) Vectors $a = i - j + k$ and $b = 2i + 3j - k$.

We know that$a \times b = i(1 - 3) - j( - 1 - 2) + k(3 + 2)$
$ = - \,2i + 3j + 5k$

and $|a \times b|\,$$ = \sqrt {{{( - 2)}^2} + {{(3)}^2} + {{(5)}^2}} = \sqrt {38} $

Therefore unit vector $\frac{{a \times b}}{{|a \times b|}} = \frac{{ - 2i + 3j + 5k}}{{\sqrt {38} }}$.

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