Question

find the unit vector in the direction of vector {7,-24}

Answer 1

The unit vector will have fractions for the x and y components of the unit vector. The numerators will be the same as for the given vector. The denominator for each of the x and y will be the length of the given vector.

Answer 2

So, can you get the length of the given vector? Think of the vecotr as starting from the origin, a basic vector. What is the length from (0, 0) to (7, -24)? Use the distance formula for 2 points. That's the denominator.

Answer 3

When you do this, you will get:

(7/d)^2 + (-24/d)^2 = 1^2 = 1

Answer 4

@comput313 ? Is this making sense now?

Answer 5

yes i think so, let me try to work it out.

Answer 6

so the unit vector will be {7/31,-24/31}?

Answer 7

Not sure where you got the 31, possibly a typo somewhere in your calculaions. Try:

(7)^2 + (-24)^2 = d^2

Answer 8

That's from:

[0 - 7]^2 + [0 - (-24)]^2 = d^2

Answer 9

shouldnt that be -7^2 then? 0-7=-7?

Answer 10

that dosent matter does it.

Answer 11

(-7)^2 will be the same as (7)^2

because you can have either:

(0 - 7)^2 or (7 - 0)^2

The order will not matter, and the distance will always be positive because it is a measurable physical concept, not implying direction like vectors. The direction of the given vector and the unit vector will be suggested by the coordinates, basically by the "numerators".

Answer 12

so it comes out to d=25

Answer 13

Yes! Good job! @comput313

Answer 14

so the unit vector is {7/25,-24/25}?

Answer 15

There you go! Once you have the unit vecotr concept down, the direction is the same as the given vecotr. It is just shortened or lengthened.

Answer 16

how could this be written in terms of i and j?

Answer 17

For a vector {a, b} you put it into:

ai + bj

The "i" and "j" are usually in bold face in books.

Answer 18

ok, thanks!

Answer 19

Good luck to you in all of your studies and thx for the recognition! @comput313


And you're welcome!