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Math

Indiana Math

Precalculus: Trigonometry: Vectors

TR.V.1

Fully covered
Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||).

TR.V.2

Fully covered
Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

TR.V.3

Fully covered
Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

TR.V.4

Fully covered
Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

TR.V.5

Fully covered
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

TR.V.6

Fully covered
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

TR.V.7

Fully covered
Solve problems involving velocity and other quantities that can be represented by vectors.