Question:
If the resultant of two vectors is equal to either of vectors, the angle between them is
If the resultant of two vectors is equal to either of vectors, the angle between them is
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Three equal vectors forming a triangle ($P, Q, R$) must have interior angles of $60^{\circ}$, but the angle between the vector directions is $180^{\circ} - 60^{\circ} = 120^{\circ}$.
Updated On: Jul 4, 2026
- $30^{0}$
- $60^{0}$
- $90^{0}$
- $120^{0}$
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The Correct Option is D
Solution and Explanation
Step 1: Concept
The magnitude of the resultant $R$ of two vectors $P$ and $Q$ is $R^{2} = P^{2} + Q^{2} + 2PQ \cos \theta$.
Step 2: Meaning
Given $P = Q = R$. Substituting these into the formula gives $P^{2} = P^{2} + P^{2} + 2P^{2} \cos \theta$.
Step 3: Analysis
$P^{2} = 2P^{2} + 2P^{2} \cos \theta \implies -P^{2} = 2P^{2} \cos \theta \implies \cos \theta = -1/2$.
Step 4: Conclusion
The angle whose cosine is $-1/2$ is $120^{\circ}$. Final Answer: (D)
The magnitude of the resultant $R$ of two vectors $P$ and $Q$ is $R^{2} = P^{2} + Q^{2} + 2PQ \cos \theta$.
Step 2: Meaning
Given $P = Q = R$. Substituting these into the formula gives $P^{2} = P^{2} + P^{2} + 2P^{2} \cos \theta$.
Step 3: Analysis
$P^{2} = 2P^{2} + 2P^{2} \cos \theta \implies -P^{2} = 2P^{2} \cos \theta \implies \cos \theta = -1/2$.
Step 4: Conclusion
The angle whose cosine is $-1/2$ is $120^{\circ}$. Final Answer: (D)
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