Question

Find the component form and magnitude of the vector v represented by the directed line segment that has initial point (4,-7) and terminal point (-1,5).

A) Component form: (-5,12); Magnitude: 13
B) Component form: (-3,10); Magnitude: 11
C) Component form: (-5,12); Magnitude: 17
D) Component form: (-3,10); Magnitude: 13

Answer 1

The vector v represented by the directed line segment from (4,-7) to (-1,5) has a component form of (-5, 12) and a magnitude of 13.

Step-by-step explanation:

To find the component form of the vector v with initial point (4,-7) and terminal point (-1,5), we subtract the coordinates of the initial point from the coordinates of the terminal point:

Δx = x2 - x1 = -1 - 4 = -5
Δy = y2 - y1 = 5 - (-7) = 12

The component form is (-5, 12).

To find the magnitude of the vector, we use the Pythagorean theorem:

Magnitude = √((-5)² + (12)²) = √(25 + 144) = √169 = 13

Therefore, the correct answer is A) Component form: (-5,12); Magnitude: 13.