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Kamini Patla
Asked: 2022-11-11T06:57:45+05:30 In:

The shortest distancebetween the lines `(x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4`isa. `sqrt(30)`b. `2sqrt(30)`c. `5sqrt(30)`d. `3sqrt(30)`
A. `sqrt30`
B. `2sqrt30`
C. `5sqrt30`
D. `3sqrt30`

The shortest distancebetween the lines `(x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4`isa. `sqrt(30)`b. `2sqrt(30)`c. `5sqrt(30)`d. `3sqrt(30)`
A. `sqrt30`
B. `2sqrt30`
C. `5sqrt30`
D. `3sqrt30`
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1 Answer

  1. Correct Answer – d
    Given lines are `vecr = 3hati + 8hatj + 3hatk + l(3hati – hatj +hatk)`
    and `vecr = – 3hati – 7hatj + 6hatk + m(-3hati + 2hatj + 4hatk)`
    Required shortest distance
    `=(|(6hati + 15hatj- 3hatk) .((3hati – hatj +hatk)xx(-3hati + 2hatj + 4hatk))|)/(|(3hati – hatj + hatk)xx(-3hati + 2hatj +4hatk)|)`
    `=(|(6 hati + 15hatj – 3hatk).(-3hati – 15hatj + 3hatk)|)/(|-6 hati – 15hatj + 3hatk|)`
    `=(36+225+9)/(sqrt(36+225+9)) = (270)/(sqrt(270)) = sqrt(270) = 3sqrt(3)`

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