Angle between the lines 2x - y - 15 = 0 and 3x + y + 4 = 0 is ...… - Vidyadip

MCQ

Angle between the lines $2x - y - 15 = 0$ and $3x + y + 4 = 0$ is .....$^o$

A
${90}$
✓
${45}$
C
${180}$
D
${60}$

✓

Answer

Correct option: B.

${45}$

b
(b)Lines are $2x - y - 15 = 0$ .....(i)
and $3x + y + 4 = 0$ ......(ii)
Here, ${m_1} = 2,\,{m_2} = - \,3$
If angle between them is $\theta $, then
$\tan \theta = \left| {\frac{{{m_1} - {m_2}}}{{1 + {m_1}{m_2}}}} \right|$ $ = \left| {\frac{{2 + 3}}{{1 - 6}}} \right| = \left| {\frac{5}{{ - 5}}} \right|$= 1
$\tan \theta = \tan \frac{\pi }{4}$ ==> $\theta = \frac{\pi }{4} = 45^\circ .$

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 "M.C.Q (1 Marks)" from STD 11 - 9. straight line→STD 11 - 9. straight line — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

In $\Delta ABC$, if $a, b, c$ are in $A.P.$ (with usual notations), identify the incorrect statements -

How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set $\{1,2,3,4,5,6\}$ ?

If $\ce{n(A) = 65, n(B)} = 32$ and $\ce{n(A ∩ B)} = 14,$ then $\ce{n(A \triangle B)}$ equals:

If $\text{z}=\frac{-2}{1+\sqrt{3}},$ then the value of $\text{arg (z)}$ is:

The graph of the conic $ x^2 - (y - 1)^2 = 1$ has one tangent line with positive slope that passes through the origin. the point of tangency being $(a, b). $ Then Eccentricity of the conic is

In the word COMBINE, the number of permutations keeping the vowels at odd places and taking all the letters is :

A complex number is pure imaginary if:

A bag contains $3$ white, $3$ black and $2$ red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is

If $\text{y}=\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}},$ then $\frac{\text{dy}}{\text{dx}}$ at x = 1 is

If $\omega ( \ne 1)$ is cube root of unity and ${(1 + \omega )^7} = A + B\omega $ ,then $A$ and $B$ equals