Fun Vector Problem?

Question

When vector A is added to vector B, which has a magnitude of 5.0, the vector representing their sum is perpendicular to A and has a magnitude that is twice that of A. What is the magnitude of A.

Im pretty much stumped, though I know the answer is 2.2. Could anyone explain? Thanks.

positive, the instructor confirmed it was 2.2.

oh and tk, the sum is twice of A, which we dont know. We know B is 5, A is still unknown.

Answer 1

if you're sure that the answer is 2.2, then resultant vector is 4.4

the 4.4 is perpendicular to the 2.2

since two vectors would make a parallelogram draw it in a graphing paper.

connect the points of 2.2 and 4.4 with a line which will look like the hypotenuse of a right triangle.
should look something like this:

___|,
|
a

if you connect "a" and the dot(coma) that is the 5.0 vector. the coordinates (0,0) is on the dot

im pretty sure of my answer. my B(the 5.0) is the line from a to ,
my A is the line pointing up. C, or the line resultant to adding A and B is the horizontal line.

Answer 2

I have a vector A going from origin to an arbituary point on the X axis. I have the summation vector going from origin to an arbituary point on the Y axis. Then I have a B vector going from origin to an arbituary point in the second quadrant.

I just pick a point for end point of A. I pick another point for the summation vector, but at the size twice of A.

Then the hypotenus will be sqrt(1^2 + 2^2)=sqrt(5)=2.236 That's the B assuming other length are 1 and 2.

You know how to sum up the vectors and how they are represented graphically, correct? You have two triangles here and they are identical. One you just drew up, and the other one just outside of it upside down.

BUT, we were working with ratio so we have to scale this up because we know B is 5.0

If 2.236:5.0 =1:x then x=5.0/2.236 = 2.236

Therefore, your vector B is 2.236