Find the acute angle between the lines 2x - y + 3 = 0 and x + y +… - Vidyadip

Question

Find the acute angle between the lines 2x - y + 3 = 0 and x + y + 2 = 0.

✓

Answer

Slpoe of line 2x - y + 3 = 0 is $\frac{-2}{-1}=\frac{-(\text{coefficient of x})}{(\text{coefficient of y})}=2$
$\therefore\text{m}_1=2 \ ...(\text{i})$
Slpoe of line x + y + 2 = 0 is $\frac{-1}{1}=\frac{-(\text{coefficient of x})}{(\text{coefficient of y})}$
$\therefore\text{m}_2=-1 \ ...(\text{ii})$
Acute angle between lines
$\theta=\tan^{-1}=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$
$=\tan^{-1}=\Big|\frac{2-(-1)}{1-(2)(-1)}\Big|$
$=\tan^{-1}=\Big|\frac{3}{1-2}\Big|=\tan^{-1}=\Big|\frac{3}{1}\Big|=\tan^{-1}|3|$

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 "5 Marks Questions" from The Straight Lines→The Straight Lines — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the sixth term of the expansion $\Big(\text{y}^\frac{1}{2}+\text{x}^\frac{1}{3}\Big)^\text{n},$ if the binomial coefficient of the third term from the end is $45.$
$[$Hint: Binomial coefficient of third term from the end $=$ Binomial coefficient of third term from beginning $= ^nC_2.]$

Sum the following series to n terms:
$\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\ .....\ +\frac{1}{(5\text{n}-4)(5\text{n}+1)}$

Prove that the perpendicular drawn from the point (4, 1) on the join of (2, -1) and (6, 5) divides it in the ratio 5:8.

Show that the area of the triangle formed by the lines $y=m_1 x, y=m_2 x$ and $y=c$ is equal to $\frac{c^2}{4}(\sqrt{33}+\sqrt{11})$, where $m_1$, $m _2$ are the roots of the equation $x ^2+(\sqrt{3}+2) x +\sqrt{3}-1=0$.

Evaluate the following limits.
$\lim\limits_{\text{y} \rightarrow 0}\frac{(\text{x}+\text{y})\sec(\text{x}+\text{y})-\text{x}\sec\text{x}}{\text{y}}$

In a $\triangle\text{ABC},$ prove that
$\sin^3\text{A}\cos(\text{B}-\text{C})+\sin^2\text{B}\cos(\text{C}-\text{A})+\sin^3\text{C}\cos(\text{A}-\text{B})\\=3\sin\text{A}\sin\text{B}\sin\text{C}$

Find the equation to the ellipse in the standard form whose minor axis is equal to the distance between foci and whose latus-rectum is $10.$

Find the equations of the circles touching $y-$axis at $(0, 3)$ and making an intercept of $8$ units on the $x-$axis.

Let$ A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}$. Verify the following identities:
$\text{A}-(\text{B}\cap\text{C})=(\text{A}-\text{B})\cup(\text{A}-\text{C})$

Find the middle terms(s) in the expansion of:
$\Big(2\text{ax}-\frac{\text{b}}{\text{x}^{2}}\Big)^{12}$