<PRE><B>Question 205585</B>
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
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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
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w dot y = |2 -1 5||0 1 0| = -1
cos(y) = -1/sqrt(30) y cosine
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w dot z = |2 -1 5||0 0 1| = 5
cos(z) = 5/sqrt(30) z cosine
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