List of top Mathematics Questions on angle between two lines

The angle between two lines in 3D space can be found using:

The angle between the lines $\dfrac{x-3}{-4} = \dfrac{y+2}{3} = \dfrac{z-1}{5}$ and $\dfrac{x-2}{2} = \dfrac{y-4}{1} = \dfrac{z+3}{3}$ is

The angle between the lines \( \frac{x-3}{1} = \frac{y+1}{-1} = \frac{z-2}{-1} \) and \( \frac{x+1}{2} = \frac{y-2}{2} = \frac{z+3}{-2} \) is

The value of the angle between two straight lines is \(y = (2 - \sqrt{3})x + 5\) and \(y = (2 + \sqrt{3})x - 7\) is

The angle between the lines, whose direction cosines \( l, m, n \) satisfy the equations \( l + m + n = 0 \) and \( 2l^{2} + 2m^{2} - n^{2} = 0 \), is

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is

What is the value of \( n \) so that the angle between the lines having direction ratios \( (1, 1, 1) \) and \( (1, 1, n) \) is \( 60^\circ \)?

The angle between the lines $x-2y+3=0$ and $2x+y-4=0$ is: