If a- and b- are two unit vectors inclined at an angle - such that a- - b- is a unit vector- then - is equal to

It is given that, |a⃗|=|b⃗|=|a⃗+b⃗|=1 We have, |a⃗+b⃗|^2 =|a⃗|^2+|b⃗|^2+2 a⃗.b⃗ ⇒ 1=1+1+2 |a⃗||b⃗|cos θ ⇒ cos θ = 1/2⇒θ =2π/3 ...

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Byju's Answer

Standard XI

Mathematics

Angle between Two Vectors

If a⃗ and b⃗ ...

Question

If $\to a$ and $\to b$ are two unit vectors inclined at an angle $θ$ such that $\to a + \to b$ is a unit vector, then $θ$ is equal to

\frac{π}{3}

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\frac{π}{4}

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\frac{π}{2}

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\frac{2 π}{3}

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Solution

The correct option is D $\frac{2 π}{3}$
It is given that, $| \to a | = | \to b | = | \to a + \to b | = 1$
We have, $| \to a + \to b |^{2} = | \to a |^{2} + | \to b |^{2} + 2 \to a . \to b$
$\Rightarrow 1 = 1 + 1 + 2 | \to a | | \to b | c o s θ \Rightarrow c o s θ = - \frac{1}{2} \Rightarrow θ = \frac{2 π}{3}$

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If →a and →b are two unit vectors inclined at an angle θ such that →a+→b is a unit vector, then θ is equal to

The correct option is D 2π3It is given that, |→a|=|→b|=|→a+→b|=1 We have, |→a+→b|2=|→a|2+|→b|2+2→a.→b ⇒1=1+1+2|→a||→b|cosθ⇒cosθ=−12⇒θ=2π3

If $\to a$ and $\to b$ are two unit vectors inclined at an angle $θ$ such that $\to a + \to b$ is a unit vector, then $θ$ is equal to