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Cross Product

Let a and b b...

Question

Let $\to a$ and $\to b$ be two unit vectors, then $\to a \times \to b$ will also be a unit vector if:

A

\to a = \to b

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B

\to a ⊥ \to b

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C

\to a | | \to b

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D

\to a = m \to b, m > 1

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Solution

The correct option is B $\to a ⊥ \to b$
Let $\to a \times \to b$ is an unit vector,
$\Rightarrow ∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣ = 1$
$\Rightarrow ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ sin θ = 1$
$\Rightarrow 1 = sin θ$
$\Rightarrow θ = 90^{\circ}$
Hence, $\to a \times \to b$ will also be an unit vector, if $\to a ⊥ \to b$

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