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Multiplication with Vectors

If O⃗A⃗=î-ĵ...

Question

If $\to O A =^i -^j$ and $\to O B =^j -^k$ , then a unit vector parpendicular to the plane $A O B$ is

A

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

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B

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

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C

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

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D

\frac{1}{\sqrt{2}} (^i +^j +^k)

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Solution

The correct option is B $\frac{1}{\sqrt{3}} (^i +^j +^k)$
$\to V = ˙ \to O A \times \to O B = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 0 0 & 1 & - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ =^i +^j +^k$
$∣ \to V ∣= \sqrt{3}$
$^V = \frac{1}{\sqrt{3}} (^i +^j +^k)$

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