Home › Worksheets › CBSE Grade 12 Math › Vector Algebra Prepared by Mohsim Digital Education
Name: _________________________
Date: _________________________
Score: _______ / 40
The magnitude of the vector 3i + 4j is 5 and the dot product of i with j is 0, so this Class 12 sheet opens with a magnitude and a perpendicular product. A unit vector (3/5)i + (4/5)j appears in the answers.
Key Takeaways
The magnitude of 3i + 4j is 5 (Q1).
The dot product of i and j is 0 (Q2).
Q4 records (3/5)i + (4/5)j.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
The magnitude of the vector 3i + 4j is
(a) 3 (b) 4 (c) 5 (d) 7
2.
The dot product of the vectors i and j is
(a) 1 (b) 0 (c) -1 (d) 2
3.
The dot product of two perpendicular vectors is
(a) 1 (b) 0 (c) -1 (d) |a||b|
4.
A unit vector in the direction of the vector 3i + 4j is
(a) 3i + 4j (b) (3/5)i + (4/5)j (c) i + j (d) 5i + 5j
5.
If a · b = |a||b|, then the angle between a and b is
(a) 0° (b) 90° (c) 180° (d) 60°
6.
The cross product of two parallel vectors is
(a) The zero vector (b) A unit vector (c) |a||b| (d) a · b
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Write the formula for the magnitude of the vector a = xi + yj.
8.
Find the magnitude of the vector 3i + 4j.
9.
Write the formula for a · b in terms of |a|, |b| and the angle θ between them.
10.
Find the dot product of the vectors i and j.
11.
Write the condition for two non-zero vectors to be perpendicular.
12.
Find a unit vector in the direction of the vector 4i + 3j.
13.
Write the magnitude of the zero vector.
14.
Find the dot product of the vector a = 2i + 3j with itself.
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 6i + 8j.
16.
Find the angle between the vectors i + j and i - j.
17.
If a = i + 2j, find the magnitude of a.
18.
Find the unit vector in the direction of the vector 5i + 12j.
19.
Two vectors a and b are perpendicular. If |a| = 3 and |b| = 4, find a · b.
20.
Show that the vectors 2i + 3j and 3i - 2j are perpendicular.
Answer Key
1. c) 5
2. b) 0
3. b) 0
4. b) (3/5)i + (4/5)j
5. a) 0°
6. a) The zero vector
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 3i + 4j?
5, option (c) in this worksheet (Q1).
What is the dot product of i and j?
0, option (b) in this worksheet (Q2).
What unit vector is recorded in the direction of 3i + 4j?
(3/5)i + (4/5)j, option (b) in this worksheet (Q4).