Midcontinent Research for Education and Learning
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Common Core Mathematics 912
Cluster
Perform operations on vectors.
Grade 912
N.VM.4.
(+) Add and subtract vectors.
N.VM.4.a.
Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
N.VM.4.b.
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
N.VM.4.c.
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 componentwise.
N.VM.5.
(+) Multiply a vector by a scalar.
N.VM.5.a.
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(v
_{x}
, v
_{y}
) = (cv
_{x}
, cv
_{y}
).
N.VM.5.b.
Compute the magnitude of a scalar multiple c
v
using c
v
 = cv. Compute the direction of c
v
knowing that when cv ≠ 0, the direction of c
v
is either along
v
(for c > 0) or against
v
(for c < 0).