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If we know the magnitude of two vectors and the angle (?) between them, how do we find the dot product?

a) Magnitude of one vector divided by the angle
b) Magnitude of both vectors multiplied by the angle
c) Magnitude of one vector multiplied by the angle
d) Magnitude of both vectors multiplied by the cosine of the angle

User Kiow
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1 Answer

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Final answer:

The dot product is found by multiplying the magnitudes of both vectors with the cosine of the angle between them. Therefore, the correct answer to the question is option d) Magnitude of both vectors multiplied by the cosine of the angle.

Step-by-step explanation:

If we know the magnitude of two vectors and the angle (θ) between them, the dot product is found using the formula:

A · B = |A| × |B| × cos(θ)

where |A| is the magnitude of vector A, |B| is the magnitude of vector B, and θ is the angle between the two vectors. The option that correctly represents this calculation is:

d) Magnitude of both vectors multiplied by the cosine of the angle

The dot product is significant in various fields like physics, where it's used to calculate the work done by a force. This form of vector multiplication is a scalar quantity, resulting in a single number that may represent, for instance, the work done in the context of a force causing a displacement along a certain direction.

User Bharel
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