To find the magnitude of a vector, square the endpoints, add them and take the square root of that number. The magnitude will always be either zero or a positive number. It is defined as the length of a vector.
Since most vectors are diagonal lines, finding the length might seem tricky. It is actually an easy process, and it can be done as long as at least one of the endpoints is known.
- Find the coordinates of the endpoints
- Use the formula to calculate the magnitude
Locate the vector on the graph and determine the endpoints. Use just one set of endpoints or, if known, both sets. An example would be an endpoint of (4, -3) or two endpoints of (2, 1) and (-3, 2).
When two endpoints are known, the formula to find magnitude is √((x2-x1)2+(y2-y1)2). If only one endpoint is known, the formula is simply √(x2+y2). Square each endpoint, perform the addition and/or subtraction and then find the square root. That final answer is the magnitude of the vector.
Using the examples given, the magnitude of a vector using (4, -3) works out to be √(42+(-3)2).The answer is √25, or 5.
For a vector with endpoints (2, 1) and (-3, 2), it works out to √((-3-2)2+(2-1)2). The answer is √26.