If three unit vector - -b- - satisfy - -b- - -0- then the angle between - and b- is

The correct option is B 2π3 We have #160; a + b = c #160;⇒| a + b #160;| #160;^ 2 =| c #160;| #160;^ 2 ⇒| a #160;| ...

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Standard XII

Physics

Vectors and Its Types

If three unit...

Question

If three unit vector $^a,^b,^c$ satisfy $^a +^b +^c =^0$ , then the angle between $^a$ and $^b$ is

\frac{π}{3}

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\frac{2 π}{3}

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\frac{π}{6}

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\frac{5 π}{6}

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Solution

The correct option is B $\frac{2 π}{3}$
We have
$\to a + \to b = - \to c$

$\Rightarrow {∣ ∣ ∣ \to a + \to b ∣ ∣ ∣}^{2} = {∣ ∣ \to c ∣ ∣}^{2}$
$\Rightarrow {∣ ∣ \to a ∣ ∣}^{2} + {∣ ∣ ∣ \to b ∣ ∣ ∣}^{2} + 2 \to a . \to b$
$= 1$
Since $\to a$ and $\to b$ are unit vectors
$\Rightarrow \to a . \to b = - \frac{1}{2}$
$\Rightarrow ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ cos θ$
Given $\to a$ and $\to b$ are unit vectors
$= - \frac{1}{2}$
So,
$\Rightarrow cos θ = - \frac{1}{2}$
$\Rightarrow θ = \frac{2 π}{3}$

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