The angle between the line √3x – y – 2 = 0 and x – √3y + 1 = 0 is - Vidyadip

MCQ

The angle between the line √3x – y – 2 = 0 and x – √3y + 1 = 0 is

A
15°
✓
30°
C
45°
D
60°

✓

Answer

Correct option: B.

30°

30°

Here, $m_1=\frac{-\sqrt{3}}{-1}=\sqrt{3}$,

$m_2=\frac{-1}{-\sqrt{3}}=\frac{1}{\sqrt{3}}$

Now, $\tan \theta=\left|\frac{\mathrm{m}_1-\mathrm{m}_2}{1+\mathrm{m}_1 \mathrm{~m}_2}\right|$

$\tan \theta=\left|\frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{1+\sqrt{3} \frac{1}{\sqrt{3}}}\right|=\left|\frac{3-1}{2 \sqrt{3}}\right|=\frac{1}{\sqrt{3}}$

$\theta=30^{\circ}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Straight Line→Straight Line — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\left|\begin{array}{lll}b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y\end{array}\right|=$

If $z_1$ and $z_2$ are two non-zero complex numbers such that $\left|z_1+z_2\right|=\left|z_1\right|+\left|z_2\right|$, then $\arg \left(z_1\right)-\arg \left(z_2\right)$ is equal to

If $1, \omega, \omega^2$ are the cube roots of unity, then $\frac{1}{1+2 \omega}+\frac{1}{2+\omega}-\frac{1}{1+\omega}=$

The value of $(1+i)^6+(1-i)^6$ is

In $(0,\ \pi)$ the number of solutions of the equation$\tan\text{x}+\tan2\text{x}+\tan3\text{x}=\tan\text{x}\tan2\text{x}\tan3\text{x}$ is :

The value of $10^{\circ} \sin 30^{\circ} \sin 50^{\circ} \sin 70^{\circ}$ is equal to

Two functions $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined as follows:
$f(x)=\left\{\begin{array}{l}0 ;(x \text { rational }) \\ 1 ;(x \text { irrational })\end{array}\right.$
$g(x)=\left\{\begin{array}{l}-1 ;(x \text { rational }) \\ 0 ;(x \text { irrational }),\end{array}\right.$
then $(gof)(e)+(fog)(\pi)=$

The equation of the common tangent of the parabolas $x^2=108 y$ and $y^2=32 x$, is

$\big(\sqrt{-2}\big)\big(\sqrt{-3}\big)$ is equal to :

If the function $f(x)=\left\{\begin{array}{cc}5 x-4, & \text { if } 0< x \leq 1 \\ 4 x^2+3 b x, & \text { if } 1< x< 2\end{array}\right.$ is continuous at every point of its domain, they value of $b$ is