Angle between Vectors
Before we see how to find the angle between two intersecting lines in three dimensional space, it is essential that we first look at how to find the angle between two vectors. I like to think of angle between two vectors as the measure of “how far away” the direction of one vector arrow is with respect to the direction of the other vector arrow, if that makes any sense. It measures how much ‘off direction’ one vector arrow is from the direction of the other vector arrow. If the vectors are in the same direction, angle between them is 0°. In the above picture, b⃗ is in the same direction as a⃗. c⃗ is just 10° off from the direction in which a⃗ is pointing, while the direction of d⃗ is 45° off from the direction of a⃗ . f⃗ is pointing exactly opposite to the direction of a⃗ . Vectors in opposite directions will make a 180° angle. The direction of e⃗ is 90° off from the direction of a⃗ . It is a vector perpendicular to a⃗ . With ‘angle between...