Topics
11. Vectors
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Algebra 1 - Precalculus

11.02 Operations with vectors

Lesson
Practice

Interactive practice questions

Which vector is the result of $a+b$a+b?

Loading Graph...
A Cartesian coordinate system with four vectors labeled $a$a, $b$b, $c$c, and $d$d. Each vector has an arrowhead indicating its direction. Vector $c$c is pointing directly to the right, vector $a$a is pointing up and to the right at an angle, vector $b$b is pointing down and to the right, and vector $d$d is pointing directly to the left. These vectors are not connected and are placed separately within the coordinate plane. Their placement and direction indicate that they likely represent different magnitudes and directions in a two-dimensional vector space.

$c$c

A

$d$d

B
Easy
< 1min

The vectors $a$a and $b$b have been graphed below.

Plot the result of $a+b$a+b on the same axes.

Easy
< 1min

Consider the two vectors $a$a and $b$b, as graphed below.

Easy
< 1min

The vectors $a$a, $b$b and $c$c have been graphed below.

Plot the result of $a+b+c$a+b+c on the same axes.

Easy
< 1min
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Outcomes

N.VM.A.3

(+) Solve problems involving velocity and other quantities that can be represented by vectors.

N.VM.B.4

(+) Add and subtract vectors.

N.VM.B.4.A

(+) Add and subtract vectors. 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.

N.VM.B.4.B

(+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

N.VM.B.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 component-wise.

N.VM.B.5

(+) Multiply a vector by a scalar.

N.VM.B.5.A

(+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise.

N.VM.B.5.B

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).

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