The scalar product of vectors is equal to the product of their lengths and the cosine of the angle between them:
vector a * vector b = | vector a | * | vector b | * cos∠ (vector a, vector b).
By condition | vector m | = 2, | vector n | = 4, cos∠ (vector m, vector n) = 30 degrees. Substitute the data on the value condition into the formula and find the dot product of the vectors m and n:
vector m * vector n = | vector m | * | vector n | * cos∠ (vector m, vector n) = 2 * 4 * cos∠30 = 8 * √3 / 2 = 8√3 / 2 = 4√3 …
Answer: vector m * vector n = 4√3.
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