Question

Let P=(−2,2) and Q=(3,4). Find the component form and magnitude of vector PQ.
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Answer 1

The component form of vector PQ is (5, 2) and its magnitude is sqrt(29).

Step-by-step explanation:

To find the component form of vector PQ, we subtract the coordinates of P from the coordinates of Q. The x-component of PQ is 3 - (-2) = 5 and the y-component is 4 - 2 = 2. So the component form of vector PQ is (5, 2).

To find the magnitude of vector PQ, we use the Pythagorean theorem. The magnitude is the square root of the sum of the squares of the components. So the magnitude of vector PQ is sqrt(5^2 + 2^2) = sqrt(29).