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) (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) (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:
*(a_{0})+(a_{1})*(a_{1}))
*(4)+(-2)*(-2)})
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
Plug in a=4 and b=2 and lets solve for c
Square each individual term
Combine like terms
Take the square root of both sides
simplify
So the length of the hypotenuse is . This verifies our answer
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