Angle Between Two Lines

Area of


Area =

s units

The general formula for the angle between two lines with direction ratios and is given by: For the first line , the direction ratios are . For the second line , the direction ratios are . Substitute these values into the formula: Thus, the angle between the lines is .

We are given the equations of two lines. The first one is a parametric equation given by: The second line is given in symmetric form as: Let the direction ratios (direction cosines) of the first line be since we get the direction ratios from the coefficients of in the equations of the first line. For the second line, the direction ratios are , since those are the coefficients in the symmetric form.
Step 1: Formula for the angle between two lines
The angle between two lines with direction ratios and is given by the formula: Substituting the values for the direction ratios of the lines: Thus, the angle between the two lines is: We see that the correct answer is because corresponds to an angle of , which is .