Calculus Volume 3 · free preview
Vectors in the Plane
Vectors are directed quantities with magnitude and direction, added componentwise and scaled by scalars, and the plane's geometry of dot products, angles, and projections begins here.
1. Vectors as directed quantities
Vectors as directed quantities
2. Addition and scalar multiplication
Addition and scalar multiplication
3. Standard basis and coordinates
Standard basis and coordinates
4. Direction angles and the unit circle
Direction angles and the unit circle
5. Vector components
The vector from P = (1, 2) to Q = (4, 6) has which components?
6. Magnitude formula
The magnitude of the vector (3, 4) equals what number?
7. Scalar multiplication effect
Multiplying the vector v by the scalar -2 does what geometrically?
8. Unit vector
The unit vector in the direction of (3, 4) equals which vector?
9. Parallelogram rule
The parallelogram rule for vector addition constructs the sum as which diagonal?
10. Component sum x
Adding (2, 3) and (-1, 4) gives a vector whose x component equals what number? Answer with a number.
11. Magnitude of scaled vector
The vector 3 times (1, 2) has magnitude 3 root 5. As a number, what is the factor multiplying root 5? Answer with a number.
12. Position vector identification
The position vector of the point (2, 5) has which components?
13. Basis vector names
The plane's standard basis vectors are i and which other letter? Answer with one lowercase letter.
14. Free vector principle
Two vectors with the same components but different locations are equal under which convention? Answer with two words.
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