The angle between lines 3 x + y = 1 and x + 3 y = 1 is

Question

The angle between lines $\sqrt{3} x + y = 1$ and $x + \sqrt{3} y = 1$ is

Smart Achievers · Accepted Answer

(1)

$Given equations of lines are$

$\sqrt{3} x + y = 1$ ...(i) and $x + \sqrt{3} y = 1$ ...(ii)

Let $m_{1}$ and $m_{2}$ be slopes of (i) and (ii), then

$m_{1} = - \sqrt{3}, m_{2} = - \frac{1}{\sqrt{3}}$

Let $θ$ be the angle between them, then

$\tan θ =$ $| \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} |$ $=$ $| \frac{- \sqrt{3} + \frac{1}{\sqrt{3}}}{1 + \sqrt{3} \cdot \frac{1}{\sqrt{3}}} |$ $=$ $| \frac{- 3 + 1}{2 \sqrt{3}} |$ $= \frac{1}{\sqrt{3}}$ $\Rightarrow$ $θ = \frac{π}{6}$

Solution

Q.
The angle between lines $\sqrt{3} x + y = 1$ and $x + \sqrt{3} y = 1$ is

1 $\frac{π}{6}$

2 $\frac{3 π}{4}$

3 $\frac{5 π}{2}$

4 $\frac{π}{3}$

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Solution

Q. The angle between lines 3x+y=1 and x+3y=1 is

1 π6

2 3π4

3 5π2

4 π3