Advertisements
Advertisements
Question
The angle between the lines 2x − y + 3 = 0 and x + 2y + 3 = 0 is
Options
90°
60°
45°
30°
180°
Advertisements
Solution
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°.
APPEARS IN
RELATED QUESTIONS
The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.
Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?
Find the equation of a line drawn perpendicular to the line `x/4 + y/6 = 1`through the point, where it meets the y-axis.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[- \frac{\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
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)
What can be said regarding a line if its slope is positive ?
What can be said regarding a line if its slope is negative?
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
The slope of a line is double of the slope of another line. If tangents of the angle between them is \[\frac{1}{3}\],find the slopes of the other line.
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
A quadrilateral has vertices (4, 1), (1, 7), (−6, 0) and (−1, −9). Show that the mid-points of the sides of this quadrilateral form a parallelogram.
Find the equation of a straight line with slope 2 and y-intercept 3 .
Find the equation of a straight line with slope − 1/3 and y-intercept − 4.
Find the equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.
Find the coordinates of the orthocentre of the triangle whose vertices are (−1, 3), (2, −1) and (0, 0).
Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text { is } \frac{2ab}{a^2 - b^2}\].
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlock wise direction through an angle of 15°. Find the equation of the line in new position.
If the slope of a line passing through the point A(3, 2) is `3/4`, then find points on the line which are 5 units away from the point A.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
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)`
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by ______.
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
The lines whose vector equations are `r = 2hati - 3hatj + 7hatk + lambda (2hati + phatj + 5hatk) and r = hati - 2hatj + 3hatk + µ(3hati + phatj + phatk)` are perpendicular for all values of λ and µ if p =
