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(75887) 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
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) 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
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