If the scalar product of two vectors A and B is 15 and the magnitudes are |A| =

If the scalar product of two vectors A and B is 15 and the magnitudes are |A| = 5 and |B| = 3, find the angle between them.

If the scalar product of two vectors A and B is 15 and the magnitudes are |A| = 5 and |B| = 3, find the angle between them.

Step 1: Understand the scalar product (dot product) formula: A · B = |A| * |B| * cos(θ).
Step 2: Identify the given values: A · B = 15, |A| = 5, |B| = 3.
Step 3: Substitute the known values into the formula: 15 = 5 * 3 * cos(θ).
Step 4: Calculate 5 * 3, which equals 15: 15 = 15 * cos(θ).
Step 5: Divide both sides by 15 to isolate cos(θ): 1 = cos(θ).
Step 6: Find the angle θ by using the inverse cosine function: θ = cos⁻¹(1).
Step 7: Determine the angle: cos⁻¹(1) equals 0°, so θ = 0°.

Scalar Product – The scalar product (or dot product) of two vectors is calculated as the product of their magnitudes and the cosine of the angle between them.
Magnitude of Vectors – The magnitude of a vector is a measure of its length, represented as |A| for vector A.
Trigonometric Functions – Understanding the relationship between angles and their cosine values is crucial for solving problems involving angles between vectors.