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Definition of Vector

If |a⃗ +b⃗|...

Question

If $| \to a + \to b | > | \to a - \to b |$ then the angle between $\to a$ and $\to b$ is

A

Acute

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B

Obtuse

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C

Right angle

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D

None

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Solution

The correct option is A Acute
$\begin{matrix} L e t t h e a n g l e b e t w e e n \to a a n d \to b b e θ {∣ ∣ ∣ \to a + \to b ∣ ∣ ∣}^{2} = {∣ ∣ \to a ∣ ∣}^{2} + {∣ ∣ ∣ \to b ∣ ∣ ∣}^{2} + 2 ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ cos θ a n d {∣ ∣ ∣ \to a - \to b ∣ ∣ ∣}^{2} = {∣ ∣ \to a ∣ ∣}^{2} + {∣ ∣ ∣ \to b ∣ ∣ ∣}^{2} - 2 ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ cos θ a c c o r d i n g t o q u e s t i o n ∣ ∣ ∣ \to a - \to b ∣ ∣ ∣ > ∣ ∣ ∣ \to a - \to b ∣ ∣ ∣ {∣ ∣ ∣ \to a - \to b ∣ ∣ ∣}^{2} > {∣ ∣ ∣ \to a - \to b ∣ ∣ ∣}^{2} ∴ 4 ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ cos θ > 0 \Rightarrow cos θ > 0 ∴ θ \in [0, \frac{π}{2}] s o, t h e a n g l e i s a c u t e a n g l e H e n c e, t h e o p t i o n A i s t h e c o r r e c t a n s w e r . \end{matrix}$

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Similar questions

| \to a + \to b | < | \to b - \to a |

then angle between

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\to b

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, then the angle between

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