Answer :

Given: - Point P(1, 0, 0) and equation of line


Let, PQ be the perpendicular drawn from P to given line whose endpoint/ foot is Q point.


Thus to find Distance PQ we have to first find coordinates of Q



x = 2λ + 1, y = – 3λ – 1, z = 8λ – 10


Therefore, coordinates of Q(2λ + 1, – 3λ – 1,8λ – 10)


Now as we know (TIP) ‘if two points A(x1,y1,z1) and B(x2,y2,z2) on a line, then its direction ratios are proportional to (x2 – x1,y2 – y1,z2 – z1)’


Hence


Direction ratio of PQ is


= (2λ + 1 – 1), ( – 3λ – 1 – 0), (8λ – 10 – 0)


= (2λ), ( – 3λ – 1), (8λ – 10)


and by comparing with given line equation, direction ratios of the given line are


(hint: denominator terms of line equation)


= (2, – 3,8)


Since PQ is perpendicular to given line, therefore by “condition of perpendicularity.”


a1a2 + b1b2 + c1c2 = 0 ; where a terms and b terms are direction ratio of lines which are perpendicular to each other.


2(2λ) + ( – 3)( – 3λ – 1) + 8(8λ – 10) = 0


4λ + 9λ + 3 + 64λ – 80 = 0


77λ – 77 = 0


λ = 1


Therefore coordinates of Q


i.e. Foot of perpendicular


By putting the value of λ in Q coordinate equation, we get




Now,


Distance between PQ


Tip: – Distance between two points A(x1,y1,z1) and B(x2,y2,z2) is given by







= 2√6 unit


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses