Calculate the dot product of vectors m and n if m = 3 n = 4 and the angle between them is 135.
| September 7, 2021 | education
The scalar product of two vectors is the product of the lengths of these vectors by the cosine of the angle between them.
(↑ a * ↑ b) = | ↑ a | * | ↑ b | * Cosα.
In our case, a = m = 3, b = n = 4, α = 135.
Cosα = Cos135 = Cos (180 – 45) = – Cos45.
Then: (↑ m * ↑ n) * (- Cos45) = 3 * 4 * (-√2 / 2) = -6 * √2.
Answer: The dot product is 6 * √2.
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