If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, wh

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Question: If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is the scalar product A · B? (2020)

Options:

Correct Answer: 30

Exam Year: 2020

Solution:

A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25

If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is the scalar product A · B? (2020)

If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is the scalar product A · B? (2020)

Step 1: Identify the magnitudes of the vectors A and B. Here, |A| = 5 and |B| = 10.
Step 2: Identify the angle between the vectors A and B. The angle is given as 60 degrees.
Step 3: Recall the formula for the scalar product (dot product) of two vectors: A · B = |A| * |B| * cos(angle).
Step 4: Substitute the values into the formula. We have |A| = 5, |B| = 10, and cos(60°) = 0.5.
Step 5: Calculate the scalar product: A · B = 5 * 10 * 0.5.
Step 6: Perform the multiplication: 5 * 10 = 50, then 50 * 0.5 = 25.
Step 7: Conclude that the scalar product A · B is 25.

Scalar Product – The scalar product (or dot product) of two vectors is calculated using the formula A · B = |A||B|cos(θ), where θ is the angle between the vectors.
Trigonometric Functions – Understanding the cosine function and its values for common angles, such as cos(60°) = 0.5.
Magnitude of Vectors – Recognizing the magnitudes of vectors |A| and |B| and how they are used in the scalar product calculation.