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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
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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`
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