If a- and b- are unit vectors- then what is the angle between a- and b- for -3a-b- to be unit vector-

The correct option is A 30^∘ nbsp; nbsp;|a|=|b|=1 √(3) a b is a unit vector. ⇒ |√(3) a b |^2=1 ⇒ 3 |a|^2 2√(3) a·b+|b|^2=1 ⇒ 3 2√(3)|a||b|cosθ+ 1=1 ⇒cosθ=√ ...

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Byju's Answer

Standard XII

Physics

Unit Vectors

If a⃗ and b⃗ ...

Question

If $\to a$ and $\to b$ are unit vectors, then what is the angle between $\to a$ and $\to b$ for $\sqrt{3} \to a - \to b$ to be unit vector?

30^{\circ}

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45^{\circ}

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60^{\circ}

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90^{\circ}

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Solution

The correct option is A $30^{\circ}$
$| \to a | = | \to b | = 1$
$\sqrt{3} \to a - \to b$ is a unit vector.
$\Rightarrow {∣ ∣ ∣ \sqrt{3} \to a - \to b ∣ ∣ ∣}^{2} = 1$
$\Rightarrow 3 | \to a |^{2} - 2 \sqrt{3} \to a \cdot \to b + | \to b |^{2} = 1$
$\Rightarrow 3 - 2 \sqrt{3} | \to a | | \to b | cos θ + 1 = 1$
$\Rightarrow cos θ = \frac{\sqrt{3}}{2}$
$\Rightarrow θ = 30^{\circ}$

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If →a and →b are unit vectors, then what is the angle between →a and →b for √3 →a−→b to be unit vector?

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If $\to a$ and $\to b$ are unit vectors, then what is the angle between $\to a$ and $\to b$ for $\sqrt{3} \to a - \to b$ to be unit vector?