Question:
The vector which have equal direction cosines are equally inclined to coordinate axes?
Answer:
Let the direction cosines of the line making an angle α with each of the coordinate axes.
So, l = cos α, m = cos α, n = cos α
We know the sum of the squares of the direction cosines is one.
=> l2 + m2 + n2 = 1
=> cos2 α + cos2 α + cos2 α = 1
=> 3cos2 α = 1
=> cos2 α = 1/3
=> cos α = ±1/√3
Thus, the direction cosines of the line, which is equally inclined to the coordinate
axes, are ±1/√3, ±1/√3, ±1/√3
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