به انگلیسی

Adding vectors and stretching them

Mathematics · Geometry · ages 15-16

Name ______________________ Date ____________

What is (8, -3) minus (2, 5) as a single column vector?
- (6, -8)
- (10, 2)
- (6, 8)
- (-6, 8)
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 is (5, 4) minus (2, 1) as a single column vector?
- (7, 5)
- (3, 3)
- (3, 5)
A route uses a = (3, 1), then b = (-1, 2), then -a. What is the total vector for the route?
- (-1, 2)
- (5, 6)
- (1, 4)
- (2, 2)
If a = (3, -4), then -a has the same length as a and points in the opposite direction. Is this true?
Circle one: True False
Vector a has length 5. What is the length of minus 2a?
Answer: ______________
Vector b has length 4. What is the length of 5b?
Answer: ______________
Zac worked out (6, 1) plus (3, 4) as (8, 5). What went wrong?
- He got 6 plus 3 wrong on the top
- He paired a top entry with a bottom entry
- He should have multiplied the vectors
- He subtracted the second vector

Answer key

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

(6, -8) · Subtract matching entries: 8 - 2 = 6 and -3 - 5 = -8, so the result is (6, -8).
(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.
(3, 3) · Subtract tops and bottoms: 3 and 3.
(-1, 2) · Add the three route vectors: (3, 1) + (-1, 2) + (-3, -1) = (-1, 2).
True · Multiplying by -1 changes every sign. The length stays the same, but the arrow reverses direction.
10 · The 2 doubles the length and the minus only flips direction.
20 · The scalar 5 multiplies the length by 5.
He got 6 plus 3 wrong on the top · The top entries give 6 + 3 = 9 and the bottom entries give 1 + 4 = 5. Zac's bottom entry is right, but his top entry 8 should be 9, so he slipped when adding 6 and 3.