Final answer:
The magnitude of vector PQ is the exact value \(\sqrt{40}\), or approximately 6.32 units when calculated using the Pythagorean theorem.
Step-by-step explanation:
To find the magnitude of the vector represented by bar (PQ) where P=(3,-4) and Q=(5,2), we need to use the Pythagorean theorem. The vector PQ can be considered the hypotenuse of a right triangle, and the difference in the x-coordinates (5 - 3) and the y-coordinates (2 - (-4)) are the lengths of the other two sides of this triangle.
First, calculate the differences:
- For x-coordinates: 5 - 3 = 2
- For y-coordinates: 2 - (-4) = 6
Next, apply the Pythagorean theorem:
v = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
v = \(\sqrt{2^2 + 6^2}\)
v = \(\sqrt{4 + 36}\)
v = \(\sqrt{40}\)
Thus, the magnitude of vector PQ is the square root of 40.
The exact magnitude is \(\sqrt{40}\), but you can also express it in decimal form, which is approximately 6.32 units.