Let a- and b- are two vectors- such that -a-3 and -b-2- If a-b- is unit vector- then the acute angle between a- and b- is

∵a b is a unit vector. ∴ |a b|=1 Sqauring both the sides, we get |a|^2+ nbsp;|b|^2 2×(a). (b)=1 ⇒ 9+4 2|a||b|cosθ=1 ⇒ 12 2·3·2cosθ=0 ⇒cosθ=1 ⇒θ=cos^ 11=0^∘ ...

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Byju's Answer

Standard XII

Physics

Work Done as Dot Product

Let a⃗ and b⃗...

Question

Let $\to a$ and $\to b$ are two vectors, such that $| \to a | = 3$ and $| \to b | = 2$ . If $\to a - \to b$ is unit vector, then the acute angle between $\to a$ and $\to b$ is ______

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Solution

$∵ \to a - \to b$ is a unit vector.
$∴ | \to a - \to b | = 1$
Sqauring both the sides, we get
$| \to a |^{2} + | \to b |^{2} - 2 \times (\to a) . (\to b) = 1$
$\Rightarrow 9 + 4 - 2 | \to a | | \to b | cos θ = 1$
$\Rightarrow 12 - 2 \cdot 3 \cdot 2 cos θ = 0$
$\Rightarrow cos θ = 1$
$\Rightarrow θ = {cos}^{- 1} 1 = 0^{\circ}$

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Let →a and →b are two vectors, such that |→a|=3 and |→b|=2. If →a−→b is unit vector, then the acute angle between →a and →b is ______

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