First slide

Equation of line in Straight lines

Question

If the angle between the lines $3 y - x + 4 = 0$ and $x + y - 6 = 0$ is q, then tan q is equal to.

Moderate

A

$\sqrt{3} + 1$
B

$\sqrt{3} - 1$
C

$2 + \sqrt{3}$
D

$3 + \sqrt{2}$

Solution

Slopes of the given lines are $\frac{1}{\sqrt{3}}$ and $- 1,$ so
$\tan θ = [\frac{\frac{1}{\sqrt{3}} + 1}{1 - \frac{1}{\sqrt{3}}}] = [\frac{\sqrt{3} + 1}{\sqrt{3} - 1}] = 2 + \sqrt{3}$

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