MHT CET · Maths · Vector Algebra
If \(\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}\) with \(|\overline{\mathrm{a}}|=3,|\overline{\mathrm{b}}|=5\) and \(|\overline{\mathrm{c}}|=7\), then angle between \(\bar{a}\) and \(\bar{b}\) is
- A \(\left(\frac{\pi}{3}\right)^c\)
- B \(\left(\frac{4 \pi}{3}\right)^c\)
- C \(\left(\frac{2 \pi}{3}\right)^c\)
- D \(\pi^{\mathrm{c}}\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{\pi}{3}\right)^c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \overline{\mathrm{a}}+\overline{\mathrm{b}}=-\overline{\mathrm{c}} \Rightarrow|\overline{\mathrm{a}}+\overline{\mathrm{b}}|^2=|\overline{\mathrm{c}}|^2 \\ & \therefore|\overline{\mathrm{a}}|^2+|\overline{\mathrm{b}}|^2+2|\overline{\mathrm{a}}||\overline{\mathrm{b}}| \cos \theta=|\overline{\mathrm{c}}|^2 \\ & \therefore(3)^2+(5)^2+2(3)(5) \cos \theta=(7)^2 \\ & \therefore \cos \theta=\frac{49-34}{30}=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{3}\end{aligned}\)
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