Question

The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is

• A. $ta{n}^{-1}(7)$
• B. $ta{n}^{-1}(-1/7)$
• C. $ta{n}^{-1}(1/7)$
• D. None of these

Answer 1

Answer: (C)

Let $P=(1,1)$ and $Q=(-3,4)$
$\therefore$ Slope of line $PQ$, $m_1=\frac{1-4}{1+3}=\frac{-3}{4}$
Given line is $x+y=3$ or $x+y-3=0$
Its slope, $m_2=-1$
Now, $tan\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$
$=\left|\frac{\frac{-3}{4}+1}{1+\frac{3}{4}}\right|=\frac{1}{7}$
$\Rightarrow \theta =ta{n}^{-1}\left(\frac{1}{7}\right)$