Cogito
AP Precalculus · Chapter 8 · Lesson 2
Vectors
Quantities with direction attached.
12 problems · about 21 minutes · AP Precalculus 4.4, 4.5
What this lesson teaches
The student performs vector operations and computes magnitude and direction.
- A vector has both magnitude and direction.
- Add vectors by components; magnitudes do not add.
- The magnitude is √(x² + y²), by Pythagoras.
Warm Up
Straightforward practice. Get the method working first.
5 problemsWhat is the magnitude of (9, 12)?
Answer 15
Why 15.
Why can magnitudes not simply be added?
Answer Direction matters, so components add rather than lengths.
Why Only components add.
Magnitude of (6, 8)?
Answer 10
Why √100.
Magnitude of (5, 12)?
Answer 13
Why √169.
(1, 5) + (4, 2). What is the y component?
Answer 7
Why 5 + 2.
Build It Up
The same ideas with more to keep track of.
3 problems4 times the vector (3, 2). What is the y component?
Answer 8
Why 4 × 2.
Magnitude of (0, 9)?
Answer 9
Why Straight up.
Is mass a vector? 1 yes, 0 no.
Answer 0
Why It has no direction.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each quantity by whether it is a vector.
Answer Vector: Velocity, Force · Not a vector: Mass, Temperature
Why A vector needs a direction as well as a size.
Magnitude of (8, 6)?
Answer 10
Why √100.
The Magnitude: What is the magnitude of the vector (3, 4)?
Answer 5
Why 5.
The Sum: (2, 3) + (5, 1). What is the x component of the sum?
Answer 7
Why 7.