Direction Cosines of a Line Passing through Two Points
The distance ...
Question
The distance of the point A(–2, 3, 1) from the line PQ through P(–3, 5, 2) which make equal angles with the axes is
A
2√3
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B
√143
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C
16√3
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D
5√3
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Solution
The correct option is B√143 Here,α=β=γ∵cos2α+cos2β+cos2γ=1∴cosα=1√3DC′sofPQare(1√3,1√3,1√3) PM = Projection of AP on PQ =|(−2+3)1√3+(3−5).1√3+(1−2)1√3|=2√3andAP=√(−2+3)2+(3−5)2+(1−2)2=√6AM=√(AP)2−(PM)2=√6−43=√143