Answer to Question #143798 in Mechanics | Relativity for Phoebe

Question #143798

If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:


1
Expert's answer
2020-11-16T06:40:46-0500

The magnitude of the sum of two vectors can be found from the cosine law applied to AOB\triangle AOB:


c=a2+b22abcos(180θ)=a2+b2+2abcosθc = \sqrt{a^2 + b^2 - 2ab\cos(180-\theta)} = \sqrt{a^2 + b^2 + 2ab\cos\theta}

where θ\theta is the angle between the vectors a\mathbf{a} and b\mathbf{b}.

Thus, it should be θ>90°\theta >90\degree for c<ac<a and c<bc<b.


Answer. If the magnitude of the sum of two vectors is less than the magnitude of either vector, then the angle between these two vectors is obtuse (>90°>90\degree ).


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