Question

In vector mathematics, vector A to B is perpendicular to vector A to P when:

A) The dot product is zero
B) The cross product is zero
C) The magnitude is zero
D) The angle between them is 90 degrees

Answer 1

Vector A to B is perpendicular to vector A to P when their dot product is zero, indicating they are orthogonal vectors with an angle of 90 degrees between them.

Step-by-step explanation:

In vector mathematics, the condition for vector A to B being perpendicular to vector A to P is that their dot product is zero. Two vectors are perpendicular, or orthogonal, when the angle between them is 90 degrees. Because cosine of 90 degrees is zero, when you compute the dot product as A · B = |A||B|cos(θ), and θ is 90 degrees, the result is 0. This indicates that the two vectors are orthogonal. The cross product being zero would mean the vectors are parallel or antiparallel, not necessarily perpendicular. Furthermore, the magnitude of a vector being zero means we are dealing with the null vector, which is a different concept.