Vectors in the Plane flashcards
31 practice cards drawn from the Vectors in the Plane lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the Vectors in the Plane lessons in full →
Which pair writes the marked vector?
(5, 2)
from “Vectors”
A vector goes 3 across and 2 up. What is the negative of it?
(-3, -2)
from “Column Vectors”
A vector goes 6 across and 5 up. What is the negative of it?
(-6, -5)
from “Column Vectors”
The drawing chains a then b. Where does the journey end?
(6, 4)
from “Adding Vectors”
(-4, -2) + (-2, 2) is what?
(-6, 0)
from “Adding Vectors”
(3, 3) − (-4, -1)
(7, 4)
from “Subtracting Vectors”
(-1, -4) − (-4, 2)
(3, -6)
from “Subtracting Vectors”
The vector a is 5 long. How long is −2 × a?
10
from “Scalar Multiplication”
The vector a is 10 long. How long is −3 × a?
30
from “Scalar Multiplication”
How long is the vector (5, 12)?
13
from “Magnitude of a Vector”
A is at (3, 3) and B at (9, 11). How long is AB?
10
from “Magnitude of a Vector”
The vector (3, 4) is 5 long. Its unit vector is what?
(0.6, 0.8)
from “Unit Vectors”
The vector (12, 16) is 20 long. Its unit vector is what?
(0.6, 0.8)
from “Unit Vectors”
Which column vector is 5i + 6j?
(5, 6)
from “The Unit Vectors i and j”
Write (4, 2) using i and j.
4i + 2j
from “The Unit Vectors i and j”
A is at (4, 3) and B at (6, 5). What is the vector from A to B?
(2, 2)
from “Position Vectors”
A is at (6, 3) and B at (3, 1). What is the vector from A to B?
(-3, -2)
from “Position Vectors”
a = (2, 2) and b = (4, 6). M is the midpoint of AB. What is OM?
(3, 4)
from “Vector Proofs with Midpoints”
P divides AB in the ratio 2 : 1, from A. What fraction of AB is A to P?
from “Vector Proofs with Midpoints”
Are (2, 3) and (7, 9) along the same line?
no
from “Collinear Vectors”
Are (4, 4) and (12, 12) along the same line?
yes
from “Collinear Vectors”
(1, 3) · (3, 5)
18
from “The Dot Product”
Which vector is perpendicular to (3, 2)?
(−2, 3)
from “The Dot Product”
Which pair is perpendicular? Check the dot products.
(1, 2) and (−2, 1)
from “The Angle Between Vectors”
Two vectors have a dot product of 0. What is the angle between them?
90°
from “The Angle Between Vectors”
How long is the vector (1, 4, 8)?
9
from “Vectors in Three Dimensions”
(3, 4, 2) + (1, 1, 1)
(4, 5, 3)
from “Vectors in Three Dimensions”
How far apart are A(1, 2, 3) and B(7, 10, 27)?
26
from “Distance and Midpoint in Three Dimensions”
A and B are 26 apart. How far is their midpoint from A?
13
from “Distance and Midpoint in Three Dimensions”
In r = (1, 1) + t(2, 2), which part sets the direction?
(2, 2)
from “The Vector Equation of a Line”
Do r = (3, 1) + t(1, 3) and r = (3, 1) + t(2, 6) draw the same line?
yes
from “The Vector Equation of a Line”