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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Calculate the dot product for vectors a = (1, 2) and b = (3, 4).
💡 Hint: Use the formula a · b = a1 * b1 + a2 * b2.
Question 2
Easy
What is the dot product of a vector with itself, for example, c = (5, 5)?
💡 Hint: Remember, the dot product of a vector with itself yields the square of its magnitude.
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 is the result of the dot product between two perpendicular vectors?
- 1
- 0
- -1
💡 Hint: Remember the geometric interpretation.
Question 2
True or False: The dot product yields a vector result.
- True
- False
💡 Hint: Think about the nature of the output.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given three vectors: a = (3, 1, 2), b = (1, 4, 0), and c = (2, -1, 3), find the dot product of a and b, and then determine the angle between c and the resultant vector of a and b.
💡 Hint: Don't forget to calculate the magnitudes for the final angle determination.
Question 2
Two vectors have a dot product of -12, Suggest possible values for their magnitudes and the angle between them.
💡 Hint: Think about how multiplying positive and negative components give a negative value?
Challenge and get performance evaluation