Cogito
Precalculus · Chapter 3 · Lesson 1
Vectors
A quantity with a direction attached.
11 problems · about 24 minutes · TEKS P.4.G, P.4.H, P.4.I
What this lesson teaches
The student adds vectors by components and finds a vector’s magnitude.
- A vector has magnitude and direction; a scalar has only magnitude.
- Vectors add component by component, with nothing mixing between them.
- The magnitude is the hypotenuse of the components.
Warm Up
Straightforward practice. Get the method working first.
4 problemsMagnitude of (9, 12)?
Answer 15
Why 15.
(1, 2) + (3, 4). x component of the sum?
Answer 4
Why 1 + 3.
Same sum. y component?
Answer 6
Why 2 + 4.
Magnitude of (3, 4)?
Answer 5
Why The 3-4-5 triangle.
Build It Up
The same ideas with more to keep track of.
3 problemsMagnitude of (5, 12)?
Answer 13
Why 25 + 144.
Scalar multiple: 3 times (2, 5). x component?
Answer 6
Why Multiply both parts.
Is speed a vector? 1 for yes, 0 for no.
Answer 0
Why No direction attached.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMagnitude of (0, 7)?
Answer 7
Why Straight up the axis.
Select every quantity that is a vector.
Answer Velocity; Force
Why Ask whether a direction is part of it.
The Sum: (2, 5) + (6, 1). What is the x component of the sum?
Answer 8
Why 8.
The Length: What is the magnitude of (6, 8)?
Answer 10
Why 10.