How Do You Calculate the Length of a Resultant Vector?

[princiebebe57]

What is the length of the resultant vector of combining 2A - 3B where vector A= 4i + 3j and vector B= 9i + 8j?

 

[J77]

First thing is to multiply the vectors by the given amounts... post your result.

 

[princiebebe57]

is it -19i + 30j?

 

[J77]

is it -19i + 30j?

No, what's 2A and 3B?

 

[princiebebe57]

2A = 8i + 6j
3B = 27i + 24j

is that correct?

 

[J77]

2A = 8i + 6j
3B = 27i + 24j

is that correct?

Yep -- now do the subtraction.

 

[princiebebe57]

so (8i + 6j)-(27i + 24j)?

 

[J77]

so (8i + 6j)-(27i + 24j)?

Yeah. What's it equal?

 

[princiebebe57]

is it -19i - 18j?

 

[J77]

is it -19i - 18j?

Yeah -- and the length (magnitude) is...

 

[princiebebe57]

i'm stuck at that!

 

[cristo]

i'm stuck at that!

The magnitude of a vector x\vec{i}+y\vec{j}=\sqrt{x^2+y^2}. So, what does give you in your case?

 

[princiebebe57]

so is it 26.172?

 

[J77]

so is it 26.172?

Yep -- to 3 decimal places.

 

[princiebebe57]

Thank you so much!

 

[Edgardo]

Hello princiebebe57,

you may find this website here interesting. It contains some questions and answers on vectors.
If you want to remember the formula for the length of a vector, it helps thinking of the Pythagorean theorem.