Q73 / 160 · TS EAMCET 2023 (14 May Shift 1) · Mathematics

If $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7$, then the angle between $\vec{a}$ and $\vec{b}$ is

  • A
    $\frac{\pi}{6}$
  • B
    $\frac{\pi}{4}$
  • Correct answer
    C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{2}$

Solution

$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$ Possible if $\vec{a}, \vec{b}, \vec{c}$ represents sides of a triangle $\begin{aligned} & |\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7 \\ & \cos \theta=\frac{a^2+b^2-c^2}{2 a b}=\frac{9+25-49}{2 \times 3 \times 5} \\ & \cos \theta=\frac{-1}{2} \Rightarrow \theta=120=\frac{2 \pi}{3} \end{aligned}$ $\therefore$ angle between $\vec{a} \& \vec{b}=(\pi-\theta)=\pi-\frac{2 \pi}{3}=\pi / 3$

Hence, the correct answer is option: 'C'.

Relevant Questions