Direction Cosines of a Line Passing through Two Points
The distance ...
Question
The distance of point A(−2,3,1) from the line PQ through P(−3,5,2), which makes 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√3 Direction cosines of PQ are (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√3 and AP=√(−2+3)2+(3−5)2+(1−2)2=√6 AM=√(AP)2−(PM)2=√6−43=√143