Question

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

• A. ${\tan }^{-1}\left(\frac{3}{7}\right)$
• B. $\pi -{\tan }^{-1}\left(\frac{3}{7}\right)$
• C. ${\tan }^{-1}\left(\frac{1}{7}\right)$
• D. $\pi -{\tan }^{-1}\left(\frac{1}{7}\right)$

Answer 1

The correct option is C ${\tan }^{-1}\left(\frac{1}{7}\right)$

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

${\tan }^{-1}\left(\frac{3}{7}\right)$ stage of given line $1y=-x+3$ is $-1$.

$\pi -{\tan }^{-1}\left(\frac{3}{7}\right)$

$\tan -1\left(\frac{1}{7}\right)$

$\pi -{\tan }^{-1}\left(\frac{1}{7}\right)$

Slope of line $-z\to$

$\frac{4-1}{-3-1}=\frac{3}{4}$

$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$

so angle is $\tan \theta =\left|\frac{-1+\frac{3}{4}}{1+\frac{3}{4}}\right|=\frac{1}{7}$

$\theta ={\tan }^{-1}\left(\frac{1}{7}\right)$