# Find the vector algebraically

## Homework Statement

Find a unit vector in the direction of the given vector w=-i-2j

## The Attempt at a Solution

-i
_______

vertical -2j_________________

Could someone please show me how I would do it grafically and algebraically?

Do I just need to find the magnitude? Wouldn't any vector that has a negative x component and a negative y component work?

square root (-1)^2+(-2)^2=square root 5

Thank you very much

## Answers and Replies

Shooting Star
Homework Helper
Any vector A divided by magnitude of A is a unit vector.

I haven't studied this in quite a while, but have you tried representing it with an Argand diagram?

http://scholar.hw.ac.uk/site/maths/topic11.asp?outline= [Broken]

Last edited by a moderator:
Thank you very much

Isn't the magnitude, in this case, the square root of 5?

So, would the unit vector be 1/square root of 5i? Aren't i and j the unit vectors? I'm already given the unit vectors, right? Don't I just need to find another one in the same direction? Thank you

Well I had a quick check of old material, but the modulus of an Argand diagram or distance from 0 is the magnitude.

if z=x+yi then $|z|=\sqrt{x^2+y^2}.$

http://www.clarku.edu/~djoyce/complex/abs.html

And then.

Like I say it's been a while but hope that helps.

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tiny-tim
Science Advisor
Homework Helper
Some straight answers …

Isn't the magnitude, in this case, the square root of 5?

So, would the unit vector be 1/square root of 5i?

Aren't i and j the unit vectors?

I'm already given the unit vectors, right? Don't I just need to find another one in the same direction? No-one gives you a straight answer, do they? Yes, the magnitude is √5. (btw, type alt-v and it gives you √)

No, you mean the unit vector is (-i - 2j)/√5.

Yes, i and j are always unit vectors in this sort of question.

Yes, you're right. Why so puzzled?

Wouldn't any vector that has a negative x component and a negative y component work?

No - I don't see why you'd think that. graphically and algebraically?

Algebraically, you've understood it fine!

Graphically: -i -2j is on the circle of radius √5; join it to the origin by a line; then you want the point where that line cuts the circle of radius 1. Thank you very much everyone

Regards

Shooting Star
Homework Helper
Isn't the magnitude, in this case, the square root of 5?

Right.

So, would the unit vector be 1/square root of 5i? Aren't i and j the unit vectors? I'm already given the unit vectors, right? Don't I just need to find another one in the same direction? i and j are unit vectors along the positive x-axis and y-axis respectively, but you can find a unit vector in any direction. In this case, the given direction was along the vector w=-i-2j. So, you have to divide w by mod(w) to get the unit vector in the direction of w.

No-one gives you a straight answer, do they? You got that right. Everybody wants to make sure the OP does learn a bit at least by doing something himself/herself.

You got that right. Everybody wants to make sure the OP does learn a bit at least by doing something himself/herself.

Including me, I just learnt how to calculate the magnitude of a vector using an Argand diagram. Again. 