Question 1192449: If vectors a, b and c are mutually perpendicular of equal magnitude, then find the angle between vectors a and a+b+c
Please kindly help me solve this.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If vectors a, b and c are mutually perpendicular of equal magnitude, then find the angle between vectors a and a+b+c
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The 3 vectors form a cube.
The sum of them is parallel to the long diagonal of a cube. If side lengths = s, that's s*sqrt(3).
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The cosine of the angle = s*sqrt(2)/(s*sqrt(3)) = sqrt(2/3) = sqrt(6)/3
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Lookup "direction cosines"
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