Question

Let $\vec{a}, \vec{b}$ and $\vec{c}$ are three non-collinear vectors in a plane such that $|\vec{a}|=2,|\vec{b}|=5$ and $|\vec{c}|=\sqrt{29}$. If the angle between $\vec{a}$ and $\vec{c}$ is $\theta_1$ and the angle between $\vec{b}$ and $\vec{c}$ is $\theta_2$, where $\theta_1, \theta_2 \in\left[\frac{\pi}{2}, \pi\right]$, then the value of $\theta_1+\theta_2$ is equal to

• A. $\frac{7 \pi }{6}$
• B. $\frac{4 \pi }{6}$
• C. $\frac{3 \pi }{2}$
• D. $\frac{7 \pi }{4}$

Answer 1

Answer: (C)

$\left|\vec{a}\right|^{2}+\left|\vec{b}\right|^{2}=\left|\vec{c}\right|^{2}$ (property of triangles)

From the diagram,
$\pi -\theta _{1}+\pi -\theta _{2}=\frac{\pi }{2}$
$\Rightarrow \theta _{1}+\theta _{2}=\frac{3 \pi }{2}$