Question

Vector Vector A B. has an initial point of (–4, 4, 0) and a terminal point of (–4, –8, 1). Vector Vector C D. has an initial point of (–5, 7, –2) and a terminal point of (1, –5, –6). What is the component form of vector Vector A B minus vector C D.?

Answer 1

The result is the vector (-6, 0, 5).To calculate the component form of vector AB minus vector CD, subtract the initial point of each vector from the terminal point, then invert the components of vector CD and add them to the components of vector AB.

Step-by-step explanation:

To find the component form of vector AB minus vector CD, we follow the rule that the subtraction of vectors is accomplished by the addition of a negative vector. Specifically, A - B = A + (-B). Therefore, we need to find the component form of both vectors, invert the components of vector CD, and then add these to the components of vector AB.

First, find the components of vector AB by subtracting the initial point from the terminal point: AB = terminalAB - initialAB = (-4+4, -8-4, 1-0) = (0, -12, 1).

Next, find the components of vector CD in the same way: CD = terminalCD - initialCD = (1+5, -5-7, -6+2) = (6, -12, -4).

Now we need the negatives of the components of vector CD to subtract: -CD = (-6, 12, 4).

Finally, add this to vector AB to find the component form of AB - CD: (0-6, -12+12, 1+4) = (-6, 0, 5).

Therefore, the component form of vector AB minus vector CD is (-6, 0, 5).

Answer 2

To find component form of vector AB minus vector CD, subtract the coordinates of each vector's initial point from its terminal point. Then, reverse the signs of vector CD's components and add them to vector AB's components. The result is the component form (-6, 0, 5).

Step-by-step explanation:

To find the component form of vector AB minus vector CD, we first need to find the components of each vector. We do this by subtracting the coordinates of the initial point from the terminal point for each vector.

For vector AB:

x-component: (-4) - (-4) = 0

y-component: (-8) - (4) = -12

z-component: (1) - (0) = 1

For vector CD:

x-component: (1) - (-5) = 6

y-component: (-5) - (7) = -12

z-component: (-6) - (-2) = -4

To subtract vector CD from vector AB, or vector AB minus vector CD, we take the negative of vector CD's components and add them to vector AB's components:

x-component: 0 + (-6) = -6

y-component: -12 + 12 = 0

z-component: 1 + 4 = 5

The component form of vector AB minus vector CD is therefore (-6, 0, 5).