The scalar product of two vectors A and B is 12, and the angle between them is 6

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Question: The scalar product of two vectors A and B is 12, and the angle between them is 60°. If |A| = 4, find |B|.

Options:

Correct Answer: 8

Solution:

A · B = |A||B|cos(θ) => 12 = 4|B|(0.5) => |B| = 6.

The scalar product of two vectors A and B is 12, and the angle between them is 60°. If |A| = 4, find |B|.

The scalar product of two vectors A and B is 12, and the angle between them is 60°. If |A| = 4, find |B|.

Step 1: Write down the formula for the scalar product of two vectors: A · B = |A| |B| cos(θ).
Step 2: Identify the values given in the problem: A · B = 12, |A| = 4, and θ = 60°.
Step 3: Calculate cos(60°). The value of cos(60°) is 0.5.
Step 4: Substitute the known values into the formula: 12 = 4 |B| (0.5).
Step 5: Simplify the equation: 12 = 2 |B|.
Step 6: Solve for |B| by dividing both sides by 2: |B| = 12 / 2.
Step 7: Calculate the final value: |B| = 6.

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