Add vector

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.

Correct answer:

x =  1
y =  1
m =  1.4142

Step-by-step explanation:

P=(5,8) Q=(6,9)  PQ =QP = (x,y)  x=QxPx=65=1
y=QyPy=98=1  PQ = (1,1)
m=PQ  m=x2+y2=12+12=2=1.4142

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What is the component form of a vector?

The component form of a vector is given as (x, y), where x describes how far right or left a vector is going, and y represents how far up or down a vector is going.

When two points are given: P (the start point of the vector) and Q (the end point of the vector), the x component of the vector is the difference of x coordinates between endpoint Q and start point P, and y is the difference between the y coordinates of end Q and start point P.

Calculating the vector's magnitude uses the Pythagorean theorem to find the length of the hypotenuse of the formed right-angled triangle. Magnitude is the square root of x2+y2. The distance formula can be used to find it from two points, P and Q.

Tips for related online calculators
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
See also our right triangle calculator.

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