5.5.4 - Dot Product (Scalar Product)
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Practice Questions
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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 \\).
Is the result of a dot product a vector or a scalar?
💡 Hint: Think about what kind of quantity a dot product yields.
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Interactive Quizzes
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What does the dot product yield?
💡 Hint: Remember, it gives a number, not a direction.
If \( \vec{A} \cdot \vec{A} = 0 \), what can be said about \( \vec{A} \)?
💡 Hint: Think about vectors and their magnitudes.
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Challenge Problems
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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.
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.
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