HSC Science (General) 12th Board ExamMaharashtra State Board
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Solution - If the lines (x-1)/-3=(y-2)/(2k)=(z-3)/2 and (x-1)/(3k)=(y-5)/1=(z-6)/-5 are at right angle then find the value of k - HSC Science (General) 12th Board Exam - Mathematics and Statistics

ConceptShortest Distance Between Two Lines

Question

If the lines

(x-1)/-3=(y-2)/(2k)=(z-3)/2 and (x-1)/(3k)=(y-5)/1=(z-6)/-5

are at right angle then find the value of k

Solution

Given equations of the line are:

Let bara and  bar b be vectors in the direction of lines (x-1)/-3=(y-2)/(2k)=(z-3)/2 and  (x-1)/(3k)=(y-5)/1=(z-6)/-5 " respectively"

therefore bar a=-3hati+2khatj+2hatk and bar b=3khati+hatj-5hatk

bar a.bar b=-9k+2k-10=-7k-10

Given lines are at right angle

theta=90^@

costheta=(bar a.bar b)/(|bara|.|barb|)

bara.barb=0

-7k-10=0

k=-10/7

Is there an error in this question or solution?

APPEARS IN

2015-2016 (March) (with solutions)
Question 1.2.5 | 2 marks

Reference Material

Solution for question: If the lines (x-1)/-3=(y-2)/(2k)=(z-3)/2 and (x-1)/(3k)=(y-5)/1=(z-6)/-5 are at right angle then find the value of k concept: Shortest Distance Between Two Lines. For the courses HSC Science (General) , HSC Science (Computer Science), HSC Science (Electronics), HSC Arts
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