Angle between two lines

We continue with the videos about the equations of the line. In the previous videos, I explained that there were different types of lines: parallel and secant. Watch video: relative positions. If we are faced with secant lines (which intersect at a point), it means that at the point where they intersect, they form an angle.

In this video we will see how find the angle formed by two lines. To find it, we will do it from the formula of the dot product that we saw in previous videos. Watch video: Scalar product

We will have to clear the cosine of the angle in the formula and we will have this:

Once this is known, we will see if the lines are parallel. Watch video: relative positions

If they are parallel we will no longer be able to calculate the angle. If they are not, we can start to calculate the angle between two lines.

You will see and understand the steps better in the video but I summarize them below:

• calculate the director vector of the first equation of the line
• calculate the director vector of the second equation of the line
• apply the formula for the cosine of the angle

To practice with exercises similar to the one I explained in class, you can do the printable exercises with their solutions that I have left you on the web.