Vector addition

[123]

Calculate vector \(\displaystyle \vec{k}+\vec{a}\) length, if \(\displaystyle \vec{k}=-3\vec{i}+10\vec{j}, \vec{a}=8\vec{i}+2\vec{j}\).

 

[DrSteve]

You add two vectors by performing addition in each component.

The length of the vector \(\displaystyle (u,v)\) is \(\displaystyle \sqrt{u^2+v^2}\).

Now see if you can answer the question.

 

[123]

so write like that: \(\displaystyle \sqrt{5^{2}+10^2}=13\)

 

[DrSteve]

The 10 should be a 12, but I think you have the right idea.

 

[Alurkz]

Just think of it as a right triangle. The vectors being added are the sides and the sum is the hypotenuse. The formula DrSteve provided is just a variation of the Pythagorean theorem. I don't know if this concept is too fundamental for your current knowledge of vectors but if you're just beginning to learn about them try this out. It helps me out so I thought I'd share.

 

[123]

The 10 should be a 12, but I think you have the right idea.

my mistake. I have in my papers write 12. :lol:

 

[123]

Just think of it as a right triangle. The vectors being added are the sides and the sum is the hypotenuse. The formula DrSteve provided is just a variation of the Pythagorean theorem. I don't know if this concept is too fundamental for your current knowledge of vectors but if you're just beginning to learn about them try this out. It helps me out so I thought I'd share.

You thinking about this: http://en.wikipedia.org/wiki/Hypotenuse
I don't know about that but i'll try to study this.