Given lines $$x-42=y+54=z-1-3$$ and $$x-21=y+13=z2$$ Statement $$S1$$: The lines intersect Statement $$S2$$: They are not parallel

Correct option is 4S1 is False, S2 is True

Questions

$Given lines \frac{x - 4}{2} = \frac{y + 5}{4} = \frac{z - 1}{- 3} and \frac{x - 2}{1} = \frac{y + 1}{3} = \frac{z}{2}$
$Statement (S_{1}) : The lines intersect$
$Statement (S_{2}) : They are not parallel$

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detailed solution

Correct option is D

let A=(4,-5,1), B=(2,-1,0) c¯=(2,4,-3),d¯=(1,3,2)then AB¯ c¯ d¯=−24−124−3132≠0∴ The lines are non−coplanarc¯ is not parallel to d¯⇒ The lines are non−parallelHence they are skew−lines

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Given lines x-42=y+54=z-1-3 and x-21=y+13=z2 Statement S1: The lines intersect Statement S2: They are not parallel

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free study material

$Given lines \frac{x - 4}{2} = \frac{y + 5}{4} = \frac{z - 1}{- 3} and \frac{x - 2}{1} = \frac{y + 1}{3} = \frac{z}{2}$
$Statement (S_{1}) : The lines intersect$
$Statement (S_{2}) : They are not parallel$