Cogito
Geometry · Chapter 7 · Lesson 2
Vectors on the Plane
Direction and distance in one object.
11 problems · about 23 minutes · G-GPE.B.7
What this lesson teaches
The student adds vectors by components and finds a magnitude.
- A vector is an x part and a y part together.
- Vectors add component by component, and the picture closes a triangle.
- The magnitude is the hypotenuse of the components.
Warm Up
Straightforward practice. Get the method working first.
4 problemsMagnitude of (8, 15)?
Answer 17
Why 17.
(1, 3) + (5, 2). x component?
Answer 6
Why 1 + 5.
Same sum. y component?
Answer 5
Why 3 + 2.
Magnitude of (6, 8)?
Answer 10
Why 36 + 64.
Build It Up
The same ideas with more to keep track of.
3 problemsMagnitude of (5, 12)?
Answer 13
Why 25 + 144.
(4, 5) + (−4, −5). x component?
Answer 0
Why They cancel.
3 times (2, 4). y component?
Answer 12
Why Multiply both parts.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMagnitude of (0, 6)?
Answer 6
Why Straight up.
Do the x and y parts mix when adding vectors? 1 for yes, 0 for no.
Answer 0
Why Separately, always.
The Sum: (4, 1) + (2, 6). What is the y component?
Answer 7
Why 7.
The Length: Magnitude of (9, 12)?
Answer 15
Why 15.