Question

How do you give the complex number form of the vector with the given initial and terminal point respectively (-2, 5) and (1, 3)?

Answer 1

`<3i, -2j>`

Explanation:

Assuming that we are given P(-2, 5) and Q(1, 3), we can use the following formula to calculate the commonly used "i and j form" of the vector:

`< (x_2-x_1)i, (y_2-y_1)j >`

Notice it's very similar to the slope formula, but written in point notation and using "<" instead of parentheses.

Now let's solve:

`< 1-(-2),3-5 >`
`< 1+2,3-5 >`
`<3i, -2j>`

Should you want to go on to find the magnitude of the vector, you would use the formula `sqrt((a)^2 + (b)^2)`, with a representing i and b representing j, but those are for more intricate problems.