A vector is a quantity with both magnitude and direction, and the vector from A to B is written AB, which equals b − a, so this Year 12 sheet opens with the defining property and the position difference. The answers record the magnitude formula √(x² + y²) and a unit length of 1.
Key Takeaways
A vector has both magnitude and direction (Q1).
The vector from A to B is AB = b − a (Q2).
Q3 records √(x² + y²) as the magnitude.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.A vector is a quantity that has
(a) both magnitude and direction(b) only magnitude(c) only direction(d) no magnitude
2.The vector from point A to point B is written as
(a) AB, which equals b − a(b) |AB|(c) a + b(d) −b
3.The magnitude of a vector (x, y) is
(a) √(x² + y²)(b) x + y(c) x² + y²(d) x − y
4.The dot product of two perpendicular vectors is
(a) 0(b) 1(c) their product(d) −1
5.The dot product of vectors a and b is given by
(a) |a||b| cos θ(b) |a||b| sin θ(c) |a| + |b|(d) |a||b|
6.A unit vector has a magnitude of
(a) 1(b) 0(c) 2(d) its own length
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Distinguish between a scalar and a vector.
8.Write the formula for the magnitude of a vector.
9.Define the dot product of two vectors.
10.When is the dot product of two vectors equal to zero?
11.What is a unit vector?
12.How do you add two vectors?
13.Write the displacement vector (3, 4) in component form.
14.What is a position vector?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Find the magnitude of the vector (3, 4).
16.Find the magnitude of the vector (6, 8).
17.Find the dot product of the vectors (1, 2) and (3, 4).
18.The vectors (1, 0) and (0, 1) are perpendicular. Find their dot product.
19.Find a unit vector in the direction of the vector (3, 4).
20.Find the magnitude of the vector (−5, 12).
Answer Key
1. a) both magnitude and direction
2. a) AB, which equals b − a
3. a) √(x² + y²)
4. a) 0
5. a) |a||b| cos θ
6. a) 1
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 two properties does a vector have?
Both magnitude and direction, option (a) in this worksheet (Q1).
What is the vector from A to B?
AB, which equals b − a, option (a) in this worksheet (Q2).
What is the magnitude of the vector (x, y)?
√(x² + y²), option (a) in this worksheet (Q3).
Stuck on a similar problem? Clear your next doubt instantly with the Doubt Solver.
Browse more free worksheets for A Level Year 12.