Advertisements
Advertisements
प्रश्न
Find the angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
Advertisements
उत्तर
The equations of the lines are
3x + 4y − 7 = 0 ... (1)
4x − 3y + 5 = 0 ... (2)
Let \[m_1 \text { and } m_2\] be the slopes of these lines.
\[m_1 = - \frac{3}{4}, m_2 = \frac{4}{3}\]
\[\because m_1 m_2 = - \frac{3}{4} \times \frac{4}{3}\]
\[ = - 1\]
Hence, the given lines are perpendicular.
Therefore, the angle between them is 90°.
APPEARS IN
संबंधित प्रश्न
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.
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
The slope of a line is double of the slope of another line. If tangent of the angle between them is `1/3`, find the slopes of the lines.
If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`
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 the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
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)?
What can be said regarding a line if its slope is zero ?
What can be said regarding a line if its slope is positive ?
Consider the following population and year graph:
Find the slope of the line AB and using it, find what will be the population in the year 2010.
By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).
Find the angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
Find the acute angle between the lines 2x − y + 3 = 0 and x + y + 2 = 0.
Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
If the slopes of the lines given by the equation ax2 + 2hxy + by2 = 0 are in the ratio 5 : 3, then the ratio h2 : ab = ______.
If x + y = k is normal to y2 = 12x, then k is ______.
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.
Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.
