SOLUTION: Hi all, I cant seem to get this next problem sorted. I need to find the direction cosines of the vector: ~w = 2~i - ~j + 5~k. (Again, the ~ symbols refer to arrows in the positiv

Question 205585: Hi all, I cant seem to get this next problem sorted. I need to find the direction cosines of the vector:
~w = 2~i - ~j + 5~k.
(Again, the ~ symbols refer to arrows in the positive direction above each value, with ~ in-between referring to the arrow being above both values together)
Any help with notes would be really good.
Thanks, -Nick.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I need to find the direction cosines of the vector:
w = 2i - j + 5k
The 3 direction cosines are the cosines of the angles between the vector and the x, y and z-axes.
Find the dot product of w with a unit vector along each axis.
Angle A = x cos
Angle B = y cos
Angle C = z cos
------
w dot x = |2 -1 5||1 0 0| = 2
2 = |w|*|x|cos(x)
|w| = sqrt(4+1+25) = sqrt(30)
cos(x) = 2/sqrt(30) x direction cosine
---------------------
w dot y = |2 -1 5||0 1 0| = -1
cos(y) = -1/sqrt(30) y cosine
--------------------
w dot z = |2 -1 5||0 0 1| = 5
cos(z) = 5/sqrt(30) z cosine

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