Question

Vector v has its initial point at (11, -4) and its terminal point at (4, -5). Write the vector in component form and find its magnitude.

A) Component Form: (-7, -1); Magnitude: 7.07
B) Component Form: (-7, 1); Magnitude: 7.07
C) Component Form: (7, 1); Magnitude: 7.07
D) Component Form: (7, -1); Magnitude: 7.07

Answer 1

The component form of the vector is (-7, -1) and its magnitude is 7.07.

Step-by-step explanation:

To find the component form of the vector, we subtract the initial point from the terminal point. In this case, the x-component is 4 - 11 = -7, and the y-component is -5 - (-4) = -1. Therefore, the component form of the vector is (-7, -1).

To find the magnitude of the vector, we use the Pythagorean theorem. The magnitude is given by √((-7)^2 + (-1)^2) = √(49 + 1) = √50 = 7.07.

Therefore, the correct answer is A) Component Form: (-7, -1); Magnitude: 7.07.