The dot product of two perpendicular vectors is always equal to 0. This is because the dot product measures the amount of overlap between two vectors, and since perpendicular vectors have no overlap, their dot product is 0.
If the dot product of two vectors is equal to 0, then the vectors are perpendicular. This is because the dot product is calculated by multiplying the components of the two vectors and then adding them together. If the result is 0, it means that the two vectors are at a 90 degree angle to each other, making them perpendicular.
The formula for calculating the dot product of two vectors, a and b, is a · b = |a||b|cosθ, where |a| and |b| represent the magnitudes of the two vectors and θ represents the angle between them.
No, the dot product cannot be used to prove that two vectors are parallel. This is because the dot product only measures the angle between two vectors, not their direction. Two vectors can have the same angle between them and still be parallel or not parallel, depending on their direction.
Yes, there are other methods for proving perpendicularity, such as using the cross product or geometric proofs. However, the dot product is often the easiest and most commonly used method for proving perpendicularity.