Question

Vector v has its initial point at (13, -7) and its terminal point at (3, -1). Write the vector in component form and find its magnitude. Round the vector’s magnitude to the nearest hundredth unit. Make sure to show all work and explain the steps.

Answer 1

The vector in component form is (-10, 6) and its magnitude is approximately 11.66 units.

Step-by-step explanation:

To write the vector in component form, we subtract the initial point coordinates from the terminal point coordinates. In this case, the x-component is 3 - 13 = -10 and the y-component is -1 - (-7) = 6. Therefore, the vector in component form is (-10, 6).

To find the magnitude of the vector, we use the formula sqrt(x^2 + y^2), where x and y are the components of the vector. In this case, the magnitude is sqrt((-10)^2 + 6^2) = sqrt(100 + 36) = sqrt(136).

Rounding to the nearest hundredth, the magnitude of the vector is approximately 11.66 units.

Answer 2

Is this what your looking for?

First compute the component form of vector u by subtracting its initial values from terminal values. 18-1=17, 6-(-12)=18. So u=(17, 18). Since v points in the opposite direction, and has a magnitude three times that of u, we multuply the u by -3 and get v=(-3*17, -3*18)=(-51, -54).