Given:

Points (2, 0), (0, 3) and the line x + y = 1.

Let us assume A (2, 0), B (0, 3) be the given points.

Now, let us find the slopes

Slope of AB = m_{1}

= \(\dfrac{ (3-0) }{ (0-2)}\)

= \( \dfrac{-3}{2}\)

Slope of the line x + y = 1 is -1

m_{2} = -1

Let θ be the angle between the line joining the points (2, 0), (0, 3) and the line x + y =

\( \dfrac{ ( \dfrac{-3}{2}+1)}{ ( \dfrac{-3}{2}+1)}\)

=\( \dfrac{1}{5}\)

θ = tan^{-1}(\( \dfrac{1}{5}\))

The acute angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1 is tan^{-1} (\( \dfrac{1}{5}\)).

Prove that the points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.

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

Find the angles between pairs of straight lines 3x – y + 5 = 0 and x – 3y + 1 = 0

Find the angles between pairs of straight lines 3x + y + 12 = 0 and x + 2y – 1 = 0

Find the equation of a line which is perpendicular to the line \( \sqrt{3}x – y + 5 = 0\) and which cuts off an intercept of 4 units with the negative direction of y-axis.