The unit vector perpendicular to both - and -k- isA- 1-3-k-B- 1-3-k-C- 1-3-k-D- 1-3-k-

The correct option is C 1√(3)( î+ĵ+k̂)n̂ = A×B|A×B| We know that cross product of two vectors is given as nbsp; A× nbsp;B = (î + ĵ) × (ĵ k̂) nbsp; = ( ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

The unit vect...

Question

The unit vector perpendicular to both $^i +^j$ and $^j -^k$ is

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

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

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

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

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Solution

The correct option is B $\frac{1}{\sqrt{3}} (-^i +^j +^k)$
$^n = \frac{\to A \times \to B}{| \to A \times \to B |}$
We know that cross product of two vectors is given as
$\to A \times \to B = (^i +^j) \times (^j -^k)$
$= (^i \times^j) + (^j \times^j) - (^i \times^k) - (^j \times^k)$
$= -^i +^j +^k$
$| \to A \times \to B | = \sqrt{3}$
$\Rightarrow^n = \frac{1}{\sqrt{3}} (-^i +^j +^k)$

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