A common question for geometry students is whether or not two vectors are orthogonal, parallel, or neither. This article will help you determine the relationship between two given vectors using a few different methods.
First, let’s start by drawing the two vectors on a graph. If they are orthogonal then you can draw them with right angles and use SOHCAHTOA to find their relationship. The hypotenuse of this right triangle is the line that connects the origin (O) to both points P(x_p = y_o). If your first method does not work, try using multiplication instead: multiply one vector against its opposite, and if it produces a zero or unit length result, these are parallel; otherwise these are neither orthogonal nor parallel.
This assumes that we have normalized our vectors so that when multiplied together there will be no scaling. An equation for this would be equation (x-a) *(y-b)=0. If the answer to that question is yes, then they are orthogonal. Otherwise, it means they’re either parallel or neither. Examples: // Vectors pointing northeast and southeast respectively Vectors A=(90,-180) B=(150,240): Parallel vectors because they do not have a common point of origin in their equations.
They don’t intersect at all which indicates there’s no way for them to be part of an overlapping region between each other where both will touch on any given edge simultaneously if you were to draw these lines on top of one another. There would always be some distance left over.
