Final answer:
The dot product of two vectors →A and →B, with an angle α between them, is the product of their magnitudes and the cosine of the angle. If vectors have components, the product is Ax × Bx + Ay × By + Az × Bz. The dot product determines the angle α using the inverse cosine function.
Step-by-step explanation:
The dot product of two vectors →A and →B is a scalar value that is calculated by multiplying the magnitudes of the vectors and the cosine of the angle, α, between them. By definition, the dot product is expressed as A · B = |A||B| cosα, where |A| and |B| represent the magnitudes of vectors A and B, and α is the angle between them. If the vectors are represented by their components, the dot product can be computed as A · B = Ax × Bx + Ay × By + Az × Bz, where Ax, Ay, Az and Bx, By, Bz are the respective components of vectors →A and →B along the coordinate axes.
The resulting scalar product can be used to find the angle between the vectors by using the inverse cosine of the expression in the equation. It is important to note that the dot product is positive when vectors are pointing in roughly the same direction (α ≤ 90°), and it is negative when they point in opposite directions (α > 90°). Moreover, if vectors are orthogonal (perpendicular to each other), their dot product is zero because cos 90° = 0.