1 - A vector and its representation
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Practice Questions
Test your understanding with targeted questions
Define a vector in your own words.
💡 Hint: Think about what makes a vector unique compared to other mathematical entities.
How do you represent a vector graphically?
💡 Hint: Remember the visual representation of arrows for vectors.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a vector?
💡 Hint: Think about what makes vectors different from scalars.
Does changing the coordinate system change the vector itself?
💡 Hint: Consider whether the essence of an object changes when viewed differently.
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Challenge Problems
Push your limits with advanced challenges
Two vectors \( \vec{a} = [3, 4] \) and \( \vec{b} = [1, 2] \) are given. Calculate the dot product and the angle between them.
💡 Hint: Use the magnitudes of both vectors and the dot product to find the angle.
A vector \( \vec{c} \) lies in the xy-plane and makes a 45-degree angle with the x-axis. If its magnitude is 10, represent \( \vec{c} \) in component form.
💡 Hint: Use trigonometric functions to resolve the vector into its components.
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