The vector (3, 4) has magnitude 5 and the sum of (2, −3) and (1, 5) is (3, 2), so this Year 10 sheet opens with a magnitude and an addition. The answers also record (3, 6) and 10 as further results.
Key Takeaways
The magnitude of (3, 4) is 5 (Q1).
(2, −3) + (1, 5) = (3, 2) (Q2).
Q3 records (3, 6).
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The vector (3, 4) has magnitude equal to what?
(a) 7(b) 5(c) 12(d) 25
2.Add the vectors (2, -3) and (1, 5).
(a) (3, 2)(b) (3, -2)(c) (1, -8)(d) (2, 3)
3.If a = (1, 2), then 3a equals what?
(a) (3, 6)(b) (4, 5)(c) (3, 2)(d) (1, 6)
4.The negative of the vector (4, -2) is which vector?
(a) (-4, -2)(b) (4, 2)(c) (-4, 2)(d) (2, -4)
5.Two vectors are parallel if one of them is what?
(a) a scalar multiple of the other(b) shorter than the other(c) perpendicular to the other(d) equal in length to the other
6.The vector (6, 8) has magnitude equal to what?
(a) 14(b) 100(c) 48(d) 10
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Add the vectors (2, 5) and (3, -1).
8.Subtract the vector (1, 4) from the vector (6, 9).
9.Find the magnitude of the vector (3, 4).
10.If p = (2, 1), write down the vector 4p.
11.State whether the vectors (2, 4) and (6, 12) are parallel.
12.Find the vector from A(1, 2) to B(4, 6).
13.If a = (2, 3) and b = (1, -2), find the vector a + b.
14.State the position vector of the point P(5, -3).
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A boat travels 30 km east then 40 km north. Find its straight-line distance from the starting point.
16.A bird flies with velocity vector (8, 6) km/h. Find its speed.
17.A point P has position vector (1, 2). It moves by the vector (4, -1). Find its new position vector.
18.A force vector is (12, 5) newtons. Find its magnitude.
19.A ship sails from A(2, 3) to B(8, 11). Find the vector AB.
20.The vectors a = (2, -1) and b = (-6, 3) are related. State the scalar k such that b = k × a.
Answer Key
1. b) 5
2. a) (3, 2)
3. a) (3, 6)
4. c) (-4, 2)
5. a) a scalar multiple of the other
6. d) 10
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the magnitude of the vector (3, 4)?
5, option (b) in this worksheet (Q1).
What is (2, −3) + (1, 5)?
(3, 2), option (a) in this worksheet (Q2).
When are two vectors parallel?
When one is a scalar multiple of the other, option (a) in this worksheet (Q5).
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