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Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
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Mathematican
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.
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.
See also our right triangle calculator.
You need to know the following knowledge to solve this word math problem:
- geometry
- analytic geometry
- vector
- arithmetic
- square root
- absolute value
- planimetrics
- Pythagorean theorem
- right triangle
Units of physical quantities:
Grade of the word problem:
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