Question

If A+B=C and A+B=C then the angle between A and B is​

Answer 1

Answer:

40°angle dear but I'm not sure

Answer 2

Note: There is mistake in question right question is: If A+B=C and |A|=|B|=|C|, find the angle between vectors A and B.

${\mathcal{\red{ANSWER}}}$

Given:

$\tt{\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}}$

$\tt{|A|=|B|=|C|}$

Then,

Taking self dot product,

$\tt{\implies \overrightarrow{C}.\overrightarrow{C}=\Big(\overrightarrow{A}+\overrightarrow{B}\Big).\Big(\overrightarrow{A}+\overrightarrow{B}\Big)}$

$\tt{\implies C^{2}=A^{2}+\overrightarrow{A}.\overrightarrow{B}+\overrightarrow{B}.\overrightarrow{A}+B^{2}}$

$\tt{\implies C^{2}=A^{2}+B^{2}+2\overrightarrow{A}.\overrightarrow{B}}$

$\sf{\implies C^{2}=A^{2}+B^{2}+2AB\cos\theta}$

Also given that A = B = C

$\tt{\implies C^{2}=C^{2}+C^{2}+2C^{2}\cos\theta}$

$\tt{\implies C^{2}=2C^{2}\;(1+\cos\theta)}$

$\tt{\implies (1+\cos\theta)=\dfrac{1}{2}}$

$\tt{\implies \cos\theta = -\dfrac{1}{2}}$

$\bf{\implies \theta = 120^{\circ}}$

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