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Geometrical Representation of a Complex Number

Unit vector p...

Question

Unit vector perpendicular to the plane passing through the points $^i -^j + 2^k, 2^i -^k$ and $2^j +^k$ is

A

\frac{2^i -^j +^k}{\sqrt{6}}

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B

\frac{2^i +^j +^k}{\sqrt{6}}

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C

\frac{2^i +^j -^k}{\sqrt{6}}

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D

None of these

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Solution

The correct option is B $\frac{2^i +^j +^k}{\sqrt{6}}$
$\begin{matrix} a (x - 1) + b (y + 1) + c (z - 2) = 0 a + b - 3 c = 0 - a + 3 b - c = 0 \frac{a}{8} = \frac{- b}{- 4} = \frac{c}{4} \frac{a}{8} = \frac{b}{4} = \frac{c}{4} \frac{a}{2} = \frac{b}{1} = \frac{c}{1} 2 (x - 1) + (y + 1) + (z - 2) = 0 2 x + y + z - 3 = 0 \frac{2^i +^j +^k}{\sqrt{6}} = u n i t v e c t o r p e r p e n i c u l a r t o p l a n e H e n e, t h e o p t i o n B i s c o r r e c t a n s w e r . \end{matrix}$

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