# How to add two perpendicular 2D vectors [closed]

• vector D = 4 cm North
• vector J = 4.5 cm West

what is D+J?

In a more general sense, how can two 2D vectors that are perpendicular to each other be added?

## closed as too localized by dmckee♦Sep 6 '12 at 13:31

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• This site does not exist to do your homework for you. If this isn't homework, then it is Too Localized. Is there something more generalized/conceptual that you would like to know? – Colin McFaul Sep 6 '12 at 2:27
• No this is a homework question that I am having trouble with and would like help from knowledgable minds. Would you count it as more generalized if I asked how to add two perpendicular 2D vectors and didn't give an example? Also there is a homework tag so I assumed it does allow homework questions. – jay Sep 6 '12 at 2:30
• @jay This is explained in a lot of textbooks. What do you don't understand about the examples given there? Show an example, what you tried and why you don't understand. Besides, this is not physics. – Bernhard Sep 6 '12 at 5:47
• Jay, our FAQ forbids us to address particular example of basic problem like this. We can answer your questions on vector mathematics on a conceptual level, though this is a concept that you mostly either do or do not get. To answer you question for yourself imagine putting a mark on the floor where you are standing and then walking first 4 meters north then 4.5 meters west (I've scaled the problem by a factor of 100 just for convenience). Where will you be relative the mark? Can you express that as a distance and direction? You've just added perpendicular vectors. – dmckee Sep 6 '12 at 13:35
• Maybe we could migrate this to math.SE? – David Z Sep 6 '12 at 17:53

You really need to look at an introductory book on vectors because any answer we give on this site can only cover a tiny bit of the properties of vectors.

Having said that: you can add any vectors by thinking of them as a movement. For example vector D means "go 4cm North" and vector J means "go 4.5cm West". Adding the vectors then just means making the two movements ie D + J = "go 4cm North and 4.5cm West". The sum D+J is the vector from the staring point to the end point shown by the dashed line. Using this method you can add any two vectors in any two directions.

This addition is exactly what Asdfsdjlka is doing in his answer. He's representing the vector by two numbers $(x, y)$ where $x$ means the direction East and $y$ means the direction North. Then D is (0, 4) i.e. zero cm East and 4 cm North and J is (-4.5, 0) i.e. -4.5 cm East and zero cm North. Representing vectors in this way is convenient for addition because for any two vectors $(x_1, y_1)$ and $(x_2, y_2)$ the sum of the two vectors is just $(x_1 + x_2, y_1 + y_2)$. This works whether the vectors are parallel, perpendicular or indeed at any angle. It also works for vectors in 3D where the vector has the form $(x, y, z)$.

Assuming in 2D coordinates, let $\vec{v}_{1}=0i+4j$ and $\vec{v}_{2}=-4.5i+0j$ then $\vec{v}_{1}+$ $\vec{v}_{2}=-4.5i+4j$

• A problem though, unless I am not understanding your answer, is I don't know how to apply that when the vectors are perpendicular. If one is positive and one negative, wouldn't they be parallel? – jay Sep 6 '12 at 2:36
• @jay, negation rotates the vector through 180 degrees, not 90 degrees. – Alfred Centauri Sep 6 '12 at 2:49
• Sorry I don't think I understand. Are you saying that you can't add two vectors that are at 90 degrees of each other? – jay Sep 6 '12 at 2:54
• @jay, no I'm not saying anything remotely resembling that. – Alfred Centauri Sep 6 '12 at 14:24