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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.
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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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