Adding vectors and stretching them

Mathematics · Geometry · ages 15-16

Name ______________________ Date ____________

What is (2, 3) + (1, 4) as a single column vector?
- (3, 7)
- (3, 5)
- (2, 12)
- (4, 7)
What is (2, 3) plus (1, 4) as a single column vector?
- (3, 7)
- (3, 5)
- (2, 12)
To walk from A to C via B, you follow a from A to B, then b from B to C. What is the vector from A to C?
- a - b
- b - a
- a + b
What is (5, 1) plus (2, 6) as a single column vector?
- (7, 5)
- (7, 7)
- (3, 7)
What does -2a do to the length and the direction of vector a?
- Doubles the length and reverses the direction
- Halves the length and keeps the direction
- Doubles the length and keeps the direction
- Keeps the length and reverses the direction
What is (5, 4) minus (2, 1) as a single column vector?
- (7, 5)
- (3, 3)
- (3, 5)
Vector a has length 5. What is the length of minus 2a?
Answer: ______________
Vector a has length 5. What is the length of -2a?
Answer: ______________
Vector b has length 4. What is the length of 5b?
Answer: ______________
Vector b has length 4. What is the length of 5b?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

(3, 7) · Add tops with tops and bottoms with bottoms: 2 + 1 = 3 and 3 + 4 = 7.
(3, 7) · Tops with tops and bottoms with bottoms: 3 and 7.
a + b · Placing b tip to tail after a gives the sum a plus b.
(7, 7) · 5 plus 2 is 7 on top and 1 plus 6 is 7 below.
Doubles the length and reverses the direction · The 2 stretches the arrow to twice its length and the minus spins it to point the opposite way.
(3, 3) · Subtract tops and bottoms: 3 and 3.
10 · The 2 doubles the length and the minus only flips direction.
10 · Multiplying by 2 doubles the length, and the minus flips the direction, so 2 x 5 = 10.
20 · The scalar 5 multiplies the length by 5.
20 · The scalar 5 multiplies the length by 5, so 5 x 4 = 20.