Question

Find the magnitude of the vector PQ→ when P = (3, -4) and Q = (-7, 2).

A) 5.83
B) 7.81
C) 10.63
D) 12.21

Answer 1

The magnitude of the vector PQ→ when P = (3, -4) and Q = (-7, 2) is approximately 11.66.

Step-by-step explanation:

To find the magnitude of a vector PQ→, we can use the distance formula. The formula for the magnitude of a vector in two dimensions is given by:

|PQ→| = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given coordinates for P and Q: P(3, -4) and Q(-7, 2), we can substitute the values into the formula:

|PQ→| = sqrt((-7 - 3)^2 + (2 - (-4))^2) = sqrt((-10)^2 + (6)^2) = sqrt(100 + 36) = sqrt(136) = 11.66

The magnitude of vector PQ→ is approximately 11.66.