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Multiplication with Vectors

If pi+qj is a...

Question

If pi+qj is a unit vector perpendicular to 4i+3j, then

A

P=

- 3 / 5

and q=-

4 / 5

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B

P=

4 / 5

and q=

3 / 5

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C

P=

2 / 5

and q=

1 / 5

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D

None

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Solution

The correct option is C P= $- 3 / 5$ and q=- $4 / 5$
$p i + q j ⊥ 4 i + 3 j$

$\Rightarrow (4 i + 3 j) (p i + q j) = 0$

$4 p + 3 q = 0$

$p q = \frac{- 3}{4}$

$∴ p i + q j = - 3 i + 4 j$

$p = \frac{- 3}{5}, q = \frac{4}{5}$

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