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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Add the vectors \(\vec{A} = 1\hat{i} + 2\hat{j}\) and \(\vec{B} = 3\hat{i} + 4\hat{j}\).
💡 Hint: Combine corresponding components.
Question 2
Easy
What happens to a vector when multiplied by a scalar of 0?
💡 Hint: Consider what multiplying by zero does.
Practice 1 more question and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the result of the dot product of two perpendicular vectors?
- 1
- 0
- Depends on the vectors
💡 Hint: Think about the relationship of angles between vectors.
Question 2
True or false: The cross product of two vectors results in a scalar.
- True
- False
💡 Hint: Consider what you learned about vector products.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors \(\vec{A} = 3\hat{i} + 4\hat{j}\, and \(\vec{B} = 5\hat{i} + 6\hat{j} + 1\hat{k}\), calculate both their dot and cross products.
💡 Hint: Break it down into component calculations for both products.
Question 2
A particle is moving along vector \(\vec{A} = 50\hat{i} + 100\hat{j}\) and is affected by a force represented by \(\vec{B} = -30\hat{i} + 20\hat{j}\). Calculate the resultant vector and discuss what this vector implies about the particle's new position.
💡 Hint: Use component addition to find the resultant direction.
Challenge and get performance evaluation