Question

A = 3i + 4j and B = 7i +24j m find a vector having the same magnitude as B and parallel to A

Answer 1

let <a,b> be the vector such that
||<a,b>|| = ||B||
<a,b> = k A, where k non zero

Answer 2

i didn't get u

Answer 3

ok, we know the vector you want is k<3,4> yes? we just need to find k so that its magnitude is the same as B. Just normalize the vector <3,4> and let k = ||B||

Answer 4

actually let k = +/- ||B||

Answer 5

The way I think of it is slightly different than I've heard people explain it, but I think it is helpful so I'll go ahead and walk through some things:

If you have a vector it has a direction and a magnitude. These are two things that can actually be multiplied and divided.

So if you find the length of a vector (pythagorean theorem) then you can divide the length out of a vector leaving you with a unit vector in the same direction since all the length has been divided out.

Now you can multiply the unit vector which is basically just a directional form of 1 times the magnitude of some other vector to point it into another direction.

Additionally you can find the length of a vector by taking the dot product of it with itself and then taking the square root. Obviously this is just a clever way of rewriting the pythagorean theorem since the dot product with itself will just square each term.

Answer 6

No let me try , and see if i get the method wait

Answer 7

In fact that's how complex numbers work. \[\Large z=r*e^{i \theta}\] r is the length of the vector and e^(i theta) is unit vector direction.

Of course, these are only 2 dimensions. But if you know a little about complex numbers, you can use this to help yourself out. If not, then whatever haha.

Answer 8

magnitude of A = 5
magnitude of B = 25

unit vector along A =