Question

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B . Write vector F in component form.

Answer 1

Answer:
`F = 16i - 22j`

Step-by-step explanation:

We know the following from the question:

`A = 4i-2j`

`B = -3i+5j`

`F=A-4B`

If we are trying to find the component form of F, we have to figure out what it is asking. We already have A as it was given, but we are looking for 4B. In this case, the number 4 is a scalar value, so all we need to do is multiply the B vector by 4. This will give us the following:

`4B=-12i+20j`

Now that we have all we need, we can find F. I am going to put it in vector form so it is easier to see. We can do the following:

`< 4,2 > - < -12,20 >`

`< 4,-2 > + < 12,-20 >`

`< 16,-22 >`

This will give us the component form of:

`F = 16i - 22j`