Question

good afternoon.. I'm Audrey and i need help for my project. my topic is about vector.
A vector is a quantity with both a magnitude and direction and we write v= as the components of it right. So how can we say that the given vectors are equal?

Answer 1

Which given vectors? Vectors can have equal magnitudes without having the exact same components a and b, as long as ||V1|| = ||V2||

Eg if V1 = <a, b> and V2 = <c, d> their magnitudes are equal if \[a^2+ b^2 = c^2+d^2\]

Answer 2

ok thank you. How to add two vectors if we have u= <u1 , u2> v=<v1 , v2>

Answer 3

You add vectors by adding individual components. For instance, if your two vectors are
<1 , 5> and <-3 , 2>
Their sum would be
<-2 , 7>
That give you an idea?

Answer 4

thus we add vectors by adding their corresponding components same with subtracting vectors right? thanks for the idea

Answer 5

Yeah, pretty much :)
<a , b> + <c , d> = <a+c , b+d>
<a , b> - <c , d> = <a-c , b-d>

Answer 6

thank you so much. I need more information about vectors. We can get the magnitude of the given vector by what formula?

Answer 7

I'm assuming you're working with two-dimensional vectors here, ok? If you need to extend it, it can readily be done. Let v be a vector where v = <a , b>
Then its magnitude is given by:
\[\large ||v|| =\sqrt{a^2+b^2}\]
Notice that the *negative* of this vector, given by -v = <-a , -b> would have the same magnitude. Can you see why? :)

Answer 8

yes it is two- dimensional vectors. Since we are getting the magnitude of the given vector the negative will become positive

Answer 9

More clearly, the square of the negative is the same as the square of the positive.
I'd like you to notice that the magnitude of a vector is a scalar, and it's never negative.

The magnitude can easily be seen in the 2d plane. The magnitude, in its simplest sense, is the length of the vector. So suppose we have the vector here: