SOLUTION: Hi all, I am having some trouble with vectors at the moment, I was hoping someone could show me how to do the following problems correctly. a) Find the distance between (2, -3, 1)

Question 204880: Hi all, I am having some trouble with vectors at the moment, I was hoping someone could show me how to do the following problems correctly.
a) Find the distance between (2, -3, 1) and (-1, 0, -3)
b) Find the maginitude of the vector ~w = 2~i - ~j + 4~k. (The ~ symbols represent an arrow above the values in the positive direction, I didnt know how to express this properly)
Any help would be great,
Thanks, -Nick.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a) Find the distance between (2, -3, 1) and (-1, 0, -3)
It's the sqrt of the sum of the squares of the differences, dx, dy and dz
d^2 = 3^2 + 3^2 + 4^2 = 9+9+16
d^2 = 34
d = sqrt(34)
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b) Find the maginitude of the vector ~w = 2~i - ~j + 4~k. (The ~ symbols represent an arrow above the values in the positive direction, I didnt know how to express this properly)
------------------
Mag = the sqrt of the sum of the squares.
r = sqrt(4 + 1 + 16)
r = sqrt(21)
r is the distance from the Origin to the endpoint of the vector.
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