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3. Vectors
Calculating Dot Product Using Components
1:53 minutesProblem 1.48a
Textbook Question
For the two vectors A and B in Fig. E1.39, find (a) the scalar product A · B
Verified step by step guidance1
Identify the magnitudes of vectors A and B from the diagram: A = 3.60 m and B = 2.40 m.
Determine the angle between vectors A and B. From the diagram, vector A makes a 70° angle with the positive x-axis, and vector B makes a 30° angle with the negative x-axis. Therefore, the angle between A and B is 70° + 30° = 100°.
Recall the formula for the scalar product (dot product) of two vectors: A · B = |A| |B| cos(θ), where |A| and |B| are the magnitudes of the vectors, and θ is the angle between them.
Substitute the known values into the formula: A · B = (3.60 m) * (2.40 m) * cos(100°).
Calculate the cosine of 100° and multiply the values to find the scalar product A · B.
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