Arizona State University| PHY 121: Univ Physics I: Mechanics|Homework 1-1| Problem 2

Learning Goal:

To practice Tactics Box 1.2 Vector Subtraction.
Vector subtraction has some similarities to the subtraction of two scalar quantities. With numbers, subtraction is the same as the addition of a negative number. For example, 5−3 is the same as 5+(−3). Similarly, A⃗ −B⃗ =A⃗ +(−B⃗ ). We can use the rules for vector addition and the fact that −B⃗ is a vector opposite in direction to B⃗  to form rules for vector subtraction, as explained in this tactics box.
The figure shows two vectors. Vector A is on the left and is directed upwards to the right. Vector B is on the right and is directed downwards to the right.

To subtract B⃗  from A⃗  (Figure 1), perform these steps:

  1. Draw A⃗ .  The figure shows vector A that is directed upwards to the right.
  2. Draw −B⃗  and place its tail at the tip of A⃗ .The figure shows two vectors. Vector A is on the left and is directed upwards to the right. Vector minus B is on the right and is directed upwards to the left. The tip of vector A and the tail of vector minus B are at the same point.
  3. Draw an arrow from the tail of A⃗ to the tip of −B⃗ . This is vector A⃗ −B⃗ .     The figure shows two vectors. Vector A is on the left and is directed upwards to the right. Vector minus B is on the right and is directed upwards to the left. The tip of vector A and the tail of vector minus B are at the same point. Vector A minus B starts at the tail of vector A and ends at the tip of vector minus B.
Part A
Draw vector C⃗ =A⃗ −B⃗  by following the steps in the tactics box above. When drawing −B⃗ , keep in mind that it has the same magnitude as B⃗  but opposite direction.
Part B
Draw vector F⃗ =D⃗ −E⃗ by following the steps in the tactics box above. When drawing −E⃗ , keep in mind that it has the same magnitude as E⃗  but opposite direction.
ANSWERS:
Part A
3
Part B
4