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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

What angle does the line segment joining (5,2) and (6,-15) subtend...

What angle does the line segment joining (5,2)(5,2) and (6,−15)(6,-15) subtend at (0,0)(0,0) ?

Options

  1. Aπ6\frac{\pi}{6}
  2. Bπ4\frac{\pi}{4}
  3. Cπ2\frac{\pi}{2}
  4. D3π4\frac{3 \pi}{4}

Correct answer

C. π2\frac{\pi}{2}

Step-by-step solution

Let point A=(5,2),B=(6,−15)\mathrm{A}=(5,2), \mathrm{B}=(6,-15) and O=(0,0)\mathrm{O}=(0,0). Slope of line OA=m1=2−05−0=25\mathrm{OA}=m_1=\frac{2-0}{5-0}=\frac{2}{5} Slope of line OB=m2=−15−06−0=−156\mathrm{OB}=m_2=\frac{-15-0}{6-0}=\frac{-15}{6} Angle between two lines with slopes m1andm2m_1 and m_2 is tan⁡(θ)=m1−m21+m1⋅m2=25−(−156)1+25⋅(−156)=25+1561−1tan⁡(θ)=∞⇒θ=π2\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}
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