If the scalar product of two vectors A and B is equal to the product of their ma

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Question: If the scalar product of two vectors A and B is equal to the product of their magnitudes, what can be inferred?

Options:

Correct Answer: They are parallel

Solution:

If A · B = |A||B|, then the angle between them is 0°, meaning they are parallel.

If the scalar product of two vectors A and B is equal to the product of their magnitudes, what can be inferred?

If the scalar product of two vectors A and B is equal to the product of their magnitudes, what can be inferred?

Step 1: Understand what the scalar product (dot product) of two vectors A and B is. It is calculated as A · B = |A||B|cos(θ), where θ is the angle between the two vectors.
Step 2: Recognize that |A| is the magnitude (length) of vector A and |B| is the magnitude of vector B.
Step 3: Note that if A · B = |A||B|, it means that the right side of the equation is equal to the left side.
Step 4: Since A · B = |A||B|cos(θ), if the two sides are equal, then cos(θ) must equal 1.
Step 5: The only angle θ for which cos(θ) = 1 is 0°.
Step 6: Conclude that if the angle between vectors A and B is 0°, then the vectors are parallel to each other.

Scalar Product – The scalar product (or dot product) of two vectors A and B is defined as A · B = |A||B|cos(θ), where θ is the angle between the vectors.
Magnitude of Vectors – The magnitude of a vector is its length, denoted as |A| for vector A and |B| for vector B.
Angle Between Vectors – If the scalar product equals the product of the magnitudes, it indicates that the cosine of the angle between the vectors is 1, which occurs when the angle is 0°.
Parallel Vectors – Vectors are parallel if they point in the same direction, which is the case when the angle between them is 0°.