If $\vec{a} + \vec{b} + \vec{c} = 0 and |\vec{a}| = 3, |\vec{b}| = 5 and |\vec{c}| = 7,$ show that the angle between $\vec{a}$ and $\vec{b}$ is 60⁰.

Solution

$\vec{a} + \vec{b} + \vec{c} = 0 \Rightarrow \vec{a} + \vec{b} = - \vec{c} \vec{a} + \vec{b} . \vec{a} + \vec{b} = - \vec{c} . - \vec{c} \vec{a} . \vec{a} + 2 \vec{a} . \vec{b} + \vec{b} . \vec{b} = \vec{c} . \vec{c} {|\vec{a}|}^{2} + 2 |\vec{a}| |\vec{b}| cosθ + {|\vec{b}|}^{2} = {|\vec{c}|}^{2} 3^{2} + 2 x 3 x 5 x cosθ + 5^{2} = 7^{2}$

$9 + 30 cosθ + 25 = 49 30 cosθ = 15 \Rightarrow cosθ = \frac{1}{2} cosθ = \cos 60 ° \Rightarrow θ = 60 °$

Hence proved.

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Vector Algebra

If $\vec{a} + \vec{b} + \vec{c} = 0 and |\vec{a}| = 3, |\vec{b}| = 5 and |\vec{c}| = 7,$ show that the angle between $\vec{a}$ and $\vec{b}$ is 60⁰.

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Vector Algebra

If a→ + b→ + c→ = 0 and a→ = 3, b→ = 5 and c→ = 7, show that the angle between a→ and b→ is 600.

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Classify the following measures as scalars and vectors.time period

Classify the following measures as scalars and vectors.distance

Classify the following measures as scalars and vectors.force

Classify the following measures as scalars and vectors.velocity

Classify the following measures as scalars and vectors.work done

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If $\vec{a} + \vec{b} + \vec{c} = 0 and |\vec{a}| = 3, |\vec{b}| = 5 and |\vec{c}| = 7,$ show that the angle between $\vec{a}$ and $\vec{b}$ is 60⁰.

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done