Q163 / 270 · NDA 2013 (Phase 2) · Mathematics
What angle does the line segment joining $(5,2)$ and $(6,-15)$ subtend at $(0,0)$ ?
- A$\frac{\pi}{6}$
- B$\frac{\pi}{4}$
- Correct answerC$\frac{\pi}{2}$
- D$\frac{3 \pi}{4}$
Solution
Let point $\mathrm{A}=(5,2), \mathrm{B}=(6,-15)$ and $\mathrm{O}=(0,0)$.
Slope of line $\mathrm{OA}=m_1=\frac{2-0}{5-0}=\frac{2}{5}$
Slope of line $\mathrm{OB}=m_2=\frac{-15-0}{6-0}=\frac{-15}{6}$
Angle between two lines with slopes $m_1$ and $m_2$ is
$\begin{aligned}
\tan (\theta) & =\frac{m_1-m_2}{1+m_1 \cdot m_2} \\
& =\frac{\frac{2}{5}-\left(-\frac{15}{6}\right)}{1+\frac{2}{5} \cdot\left(-\frac{15}{6}\right)}=\frac{\frac{2}{5}+\frac{15}{6}}{1-1} \\
\tan (\theta) & =\infty \Rightarrow \theta=\frac{\pi}{2}
\end{aligned}$
Hence, the correct answer is option: 'C'.