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Question

Find the direction cosines of the sides of the triangle whose vertices are (3,5,2),(1,1,2) and (5,5,2). What type of triangle is it?

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Solution

Direction ratios of :
AB=(4,4,4)BC=(8,10,0)CA=(4,6,4)
Directions of
AB=(13,13,13)BC=(441,541,0)CA=(217,317,217)
angle between,
AB&BC=cos1(13.441+13.541)=cos1(9123)BC&CA=cos1(441.217+541.317)=cos1(23697)AB&CA=cos1(217.13+13.317217.13)=cos1(351)
All angles different therefore triangle is scalene.

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