Vectors — Drills
Vectors has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
- Vector — A quantity with both magnitude and direction.
- Scalar — A quantity with size only, such as mass or temperature.
- Magnitude — The length of the vector, written |v|.
- Resultant — The single vector that two or more vectors add up to.
Adding
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For u=⟨ -5,4⟩ and v=⟨ 1,-6⟩, find the first component of u+v.
Worked answer
-4
-5+1 = -4
Problem 2
For u=⟨ -1,2⟩ and v=⟨ -7,7⟩, find the second component of u+v.
Worked answer
9
2+7 = 9
Magnitude
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the magnitude of ⟨ -6, -8 ⟩.
Worked answer
10
√36+64 = 10
Problem 2
Find the magnitude of ⟨ 5, 12 ⟩.
Worked answer
13
√25+144 = 13
Dot
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find ⟨ -4, 4 ⟩ · ⟨ 1, -5 ⟩.
Worked answer
-24
-4(1) + 4(-5)
= -4 + -20 = -24
Problem 2
Find ⟨ -1, 1 ⟩ · ⟨ -6, 6 ⟩.
Worked answer
12
-1(-6) + 1(6)
= 6 + 6 = 12
Perpendicular lines
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Are ⟨ 8, 6 ⟩ and ⟨ -6, 8 ⟩ perpendicular?
- Yes
- No
- Only if scaled
- Cannot tell
Worked answer
Yes
8(-6)+6(8) = 0
Zero means a right angle
Problem 2
Are ⟨ 1, 5 ⟩ and ⟨ 4, 2 ⟩ perpendicular?
- Yes
- No
- Only if scaled
- Cannot tell
Worked answer
No
1(4)+5(2) = 14
Not zero, so not perpendicular
Finding the constant
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find k so that ⟨ 5, k ⟩ is perpendicular to ⟨ 2, 2 ⟩.
Worked answer
-5
10 + 2k = 0
k = -5
Problem 2
Find k so that ⟨ 9, k ⟩ is perpendicular to ⟨ 8, 2 ⟩.
Worked answer
-36
72 + 2k = 0
k = -36
Resultant
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two forces, 3 N east and 4 N north, act on a point. Find the magnitude of the resultant.
Worked answer
5
√9+16 = 5
Problem 2
Two forces, 5 N east and 12 N north, act on a point. Find the magnitude of the resultant.
Worked answer
13
√25+144 = 13