If - b- are unit vectors such that -b- is also a unit vector then the angle between the vectors - and b- is

The correct option is D 2π3 We have |a+b|^2=1 ⇒ a^2+b^2+2a.b=1 ⇒ 2+2a.b=1 ⇒ 2a.b= 1 ⇒a.b= 12 ⇒ a.bcos(θ)= 12 ⇒ (1)(1)cos ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

If â, b̂ ...

Question

If $^a$ , $^b$ are unit vectors such that $^a +^b$ is also a unit vector then the angle between the vectors $^a$ and $^b$ is

\frac{π}{6}

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\frac{π}{4}

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\frac{π}{3}

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\frac{2 π}{3}

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Solution

The correct option is D $\frac{2 π}{3}$
We have
$| ¯ ¯ ¯ a + ¯ ¯ b |^{2} = 1$
$\Rightarrow a^{2} + b^{2} + 2 ¯ ¯ ¯ a . ¯ ¯ b = 1$
$\Rightarrow 2 + 2 ¯ ¯ ¯ a . ¯ ¯ b = 1$
$\Rightarrow 2 ¯ ¯ ¯ a . ¯ ¯ b = - 1$
$\Rightarrow ¯ ¯ ¯ a . ¯ ¯ b = \frac{- 1}{2}$
$\Rightarrow a . b cos (θ) = \frac{- 1}{2}$
$\Rightarrow (1) (1) cos (θ) = \frac{- 1}{2}$
$\Rightarrow θ = \frac{2 π}{3}$

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If ^a, ^b are unit vectors such that ^a+^b is also a unit vector then the angle between the vectors ^a and ^b is

The correct option is D 2π3We have|¯¯¯a+¯¯b|2=1⇒a2+b2+2¯¯¯a.¯¯b=1⇒2+2¯¯¯a.¯¯b=1⇒2¯¯¯a.¯¯b=−1⇒¯¯¯a.¯¯b=−12⇒a.bcos(θ)=−12⇒(1)(1)cos(θ)=−12⇒θ=2π3

If $^a$ , $^b$ are unit vectors such that $^a +^b$ is also a unit vector then the angle between the vectors $^a$ and $^b$ is