Question

Vector u has its initial point at (15, 22) and its terminal point at (5, -4). Vector v points in a direction opposite that of u, and its magnitude is twice the magnitude of u. What is the component form of v? A. v=<-20, 36> B. v=<-20, 56> C. v=<20, 36> D. v=<20, 52>

Answer 1

To find the component form of vector v, subtract the coordinates of the initial and terminal points of vector u. The x component of v is -20 and the y component is -52.

Step-by-step explanation:

The component form of a vector represents its x and y components. To find the x component, subtract the x-coordinate of the initial point from the x-coordinate of the terminal point. To find the y component, subtract the y-coordinate of the initial point from the y-coordinate of the terminal point.

In this case, the x component of vector u is 5 - 15 = -10, and the y component is -4 - 22 = -26.

Since vector v points in the opposite direction of vector u and has twice the magnitude, its x component will be -10 * 2 = -20, and its y component will be -26 * 2 = -52.

Therefore, the component form of vector v is v = <-20, -52>.