Q241 / 270 · NDA 2013 (Phase 2) · Mathematics

What is the angle between the lines $x+y=1$ and $x-y=1 ?$

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

Solution

Slope of line $x+y=1 \Rightarrow y=-x+1$ $m_2=-1$ Slope of line $x-y=1 \Rightarrow y=x-1$ $m_2=1$ Angle between two lines $\begin{aligned} \tan (\theta) & =\frac{m_1-m_2}{1+m_1 \cdot m_2} \\ & =\frac{1-(-1)}{1+(-1) \cdot 1}=\frac{2}{0}=\infty \end{aligned}$ Hence, $\theta=90^{\circ}$.

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

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