SOLUTION: Find the magnitude of the following vector: v=4i-2j

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Question 88187: Find the magnitude of the following vector: v=4i-2j
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
Find the magnitude of the following vector: v=4i-2j
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r = sqrt(4^2 + (-2)^2)
r = sqrt(20)
r = 2sqrt5
=============
Cheers,
Stan H.

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
To calculate the norm of the vector use the following formula:

where is the dot product of the given vector with itself

Remember the dot product of the vector with itself is:




Calculate the dot product of the radicand

Multiply

Add

Simplify if possible

So



Check:
Lets use Pythagorean's Theorem to check our work

Notice if we draw the vector we get
drawing%28500%2C+500%2C+-5%2B2%2C+5%2B2%2C+-5%2B2%2C+5%2B2%2C%0D%0Agraph%28500%2C+500%2C+-5%2B2%2C+5%2B2%2C+-5%2B2%2C+5%2B2%2C+0%29%2C%0D%0Agreen%28line%280%2C0%2C4%2C0%29%29%2C%0D%0Agreen%28line%284%2C0%2C4%2C-2%29%29%2C%0D%0Aarrow%280%2C0%2C4%2C-2%29%0D%0A%29 Plot of the vector (black line) with the vector components (green)
We can see that the vector has x and y components, which form the legs of the triangle. We can also see that the legs are 4 units and 2 units

Since we have a triangle with legs of 4 , 2 and a hypotenuse of x(our unknown side), we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
a%5E2%2Bb%5E2=c%5E2

4%5E2%2B2%5E2=c%5E2 Plug in a=4 and b=2 and lets solve for c
1+6+%2B+4+=++c++%5E+2 Square each individual term



2+0+=++c++%5E+2 Combine like terms


s+q+r+t+%28+2+0+%29+=+s+q+r+t+%28++c++%5E+2+%29 Take the square root of both sides

2%2Asqrt%285%29=c simplify

So the length of the hypotenuse is 2%2Asqrt%285%29. This verifies our answer