हिंदी

The Angle Between the Lines 2x − Y + 3 = 0 and X + 2y + 3 = 0 is - Mathematics

Advertisements
Advertisements

प्रश्न

The angle between the lines 2x − y + 3 = 0 and x + 2y + 3 = 0 is

विकल्प

  •  90°

  •  60°

  •  45°

  •  30°

  •  180°

MCQ
Advertisements

उत्तर

 90°

Let \[m_1 \text { and } m_2\] be the slope of the lines 2x − y + 3 = 0 and x + 2y + 3 = 0, respectively.
Let \[\theta\] be the angle between them.

Here, 

\[m_1 = 2 \text { and } m_2 = - \frac{1}{2}\]

\[\because m_1 m_2 = - 1\]

Therefore, the angle between the given lines is 90°.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: The straight lines - Exercise 23.21 [पृष्ठ १३४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.21 | Q 24 | पृष्ठ १३४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).


Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.


Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is 

  1. Parallel to the x-axis,
  2. Parallel to the y-axis,
  3. Passing through the origin.

Find the slope of a line passing through the following point:

 (−3, 2) and (1, 4)


Find the slope of a line passing through the following point:

\[(a t_1^2 , 2 a t_1 ) \text { and } (a t_2^2 , 2 a t_2 )\]


State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (5, 6) and (2, 3); through (9, −2) and (6, −5)


State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)


What is the value of y so that the line through (3, y)  and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?


Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).


Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.


Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.


Find the angle between the X-axis and the line joining the points (3, −1) and (4, −2).


Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. 


Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.


Find the equation of a straight line  with slope − 1/3 and y-intercept − 4.


Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.


Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.


Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).


Find the angles between the following pair of straight lines:

3x + 4y − 7 = 0 and 4x − 3y + 5 = 0


Find the angles between the following pair of straight lines:

(m2 − mn) y = (mn + n2) x + n3 and (mn + m2) y = (mn − n2) x + m3.


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


Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.


The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is 


The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is


If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?


If x + y = k is normal to y2 = 12x, then k is ______.


Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.


A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.


The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.


Show that the tangent of an angle between the lines `x/a + y/b` = 1 and `x/a - y/b` = 1 is `(2ab)/(a^2 - b^2)`


If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.


Slope of a line which cuts off intercepts of equal lengths on the axes is ______.


The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.


The point (4, 1) undergoes the following two successive transformations: 
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.


Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.


If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.


Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).


The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and

Column C1 Column C2
(a) Through the point (2, 1) is (i) 2x – y = 4
(b) Perpendicular to the line (ii) x + y – 5
= 0 x + 2y + 1 = 0 is
(ii) x + y – 5 = 0
(c) Parallel to the line (iii) x – y –1 = 0
3x – 4y + 5 = 0 is
(iii) x – y –1 = 0
(d) Equally inclined to the axes is (iv) 3x – 4y – 1 = 0

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×