Final answer:
The dot product of vectors →A and →B can be calculated by multiplying their respective components and adding the products together, or by multiplying their magnitudes and the cosine of the angle between them.
Step-by-step explanation:
The dot product (or scalar product) of two vectors →A and →B can be written in component form. If vector →A has components Ax, Ay, Az and vector →B has components Bx, By, Bz in a 3-dimensional space, then the dot product →A.→B is given as:
→A.→B = Ax × Bx + Ay × By + Az × Bz
This is also true for 2-dimensional vectors with just the x and y components. It can also be expressed in magnitude and angle form as →A.→B = |A||B| × cos(θ), where |A| and |B| are the magnitudes of the vectors and θ is the angle between them. However, when vectors are given in their component form, the component approach is straightforward and eliminates the need to calculate angles.
In addition, if the vectors are perpendicular, the component of one along the direction of the other is zero, as the dot product in this case would be zero too.