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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the dot product of \( \vec{A} = (1, 2) \) and \( \vec{B} = (3, 4) \)?
💡 Hint: Use the formula \\( A_xB_x + A_yB_y \\).
Question 2
Easy
Is the result of a dot product a vector or a scalar?
💡 Hint: Think about what kind of quantity a dot product yields.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the dot product yield?
- A vector
- A matrix
- A scalar
💡 Hint: Remember, it gives a number, not a direction.
Question 2
If \( \vec{A} \cdot \vec{A} = 0 \), what can be said about \( \vec{A} \)?
- True
- False
💡 Hint: Think about vectors and their magnitudes.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given two vectors, \( \vec{A} = (2, 3, 4) \) and \( \vec{B} = (-1, 0, 5) \), find \( \vec{A} \cdot \vec{B} \) and interpret the result in terms of direction.
💡 Hint: Apply the dot product formula and sum the results carefully.
Question 2
If \( |\vec{A}| = 5 \) and \( |\vec{B}| = 12 \) with an angle of \( 60^\circ \) between them, calculate \( \vec{A} \cdot \vec{B} \)
💡 Hint: Use the cosine value and multiply it with the magnitudes.
Challenge and get performance evaluation