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Mathematics Question on Vector Algebra

Ifa⃗.b⃗ = −∣a⃗∣ ∣b⃗∣\vec{a}.\vec{b}\, = \,- |\vec{a}| \, |\vec{b}| then the angle between a⃗\vec{a} and b⃗ \vec{b} is

A

60∘60^\circ

B

45∘45^\circ

C

180∘180^\circ

D

90∘90^\circ

Answer

180∘180^\circ

Explanation

Solution

Given, a⃗⋅b⃗=−∣a⃗∣∣b⃗∣\vec{ a } \cdot \vec{ b }=-|\vec{ a }||\vec{ b }| ⇒∣a⃗∣∣b⃗∣cos⁡θ=−∣a⃗∣∣b⃗∣\Rightarrow |\vec{ a }||\vec{ b }| \cos \theta =-|\vec{ a }||\vec{ b }| ⇒cos⁡θ=−1\Rightarrow \cos \theta =-1 ⇒θ=180∘\Rightarrow \theta =180^{\circ}