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Test for Collinearity of Vectors

A unit vector...

Question

A unit vector parallel to $x y$ plane and perpendicular to the vector $4^i - 3^j +^k$ is

A

\pm \frac{(^i +^j +^k)}{\sqrt{3}}

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B

\pm \frac{^i +^j}{5}

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C

\pm \frac{3^i + 4^j}{5}

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D

\pm \frac{3^i - 4^j}{5}

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Solution

The correct option is C $\pm \frac{3^i + 4^j}{5}$
$\begin{matrix} L e t t h e v e c t o r b e x^i + y^j (x^i + y^j) . (4^i - 3^j +^k) = 0 4 x - 3 y = 0 x^{2} + y^{2} = 1 x^{2} + \frac{16 x^{2}}{9} = 1 \frac{25 x^{2}}{9} = 1 x = \pm \frac{3}{5} x = \frac{3}{5}, y = \frac{4}{5} x = \frac{- 3}{5}, y = \frac{- 4}{5} R e q u i r e d v e c t o r = \pm \frac{3^i + 4^j}{5} H e n c e, t h e o p t i o n C i s c o r r e c t . \end{matrix}$

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