(B) The slope of the line $mx + 2y + 1 = 0$ is $m_1 = -\frac{m}{2}$.The slope of the line $2x + 3y + 5 = 0$ is $m_2 = -\frac{2}{3}$.Since the lines ar

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(B) The slope of the line $mx + 2y + 1 = 0$ is $m_1 = -\frac{m}{2}$.The slope of the line $2x + 3y + 5 = 0$ is $m_2 = -\frac{2}{3}$.Since the lines are perpendicular,the product of their slopes must be $-1$,so $m_1 \times m_2 = -1$.Substituting the values: $\left( -\frac{m}{2} \right) \times \left( -\frac{2}{3} \right) = -1$.$\frac{m}{3} = -1$.Therefore,$m = -3$.

Class 11 Mathematics Straight Line Angle between two straight lines

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If the lines $mx + 2y + 1 = 0$ and $2x + 3y + 5 = 0$ are perpendicular to each other,then what is the value of $m$?

A
$3$
B
$-3$
C
$-1/3$
D
$1/3$

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Straight Line

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Angle between two straight lines

The line passing through the points $(3, -4)$ and $(-2, 6)$ and the line passing through $(-3, 6)$ and $(9, -18)$ are:

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

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The angle between the straight lines $x - y\sqrt{3} = 5$ and $\sqrt{3}x + y = 7$ is ............. $^\circ$.

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If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2},$ find the slope of the other line.

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The acute angle between the line $4x - 2y + 13 = 0$ and the line which makes equal intercepts with the coordinate axes is

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If the lines $mx + 2y + 1 = 0$ and $2x + 3y + 5 = 0$ are perpendicular to each other,then what is the value of $m$?

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The line passing through the points $(3, -4)$ and $(-2, 6)$ and the line passing through $(-3, 6)$ and $(9, -18)$ are:

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

The angle between the straight lines $x - y\sqrt{3} = 5$ and $\sqrt{3}x + y = 7$ is ............. $^\circ$.

If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2},$ find the slope of the other line.

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