Consider the line \( L_{1}: x=y=z \) and the line \( L_{2}: 2 x+y+z-1=0= \) \( 3 x+y+2 z-2 \), t...

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Consider the line \( L_{1}: x=y=z \) and the line \( L_{2}: 2 x+y+z-1=0= \) \( 3 x+y+2 z-2 \), then:
(a) The shortest distance between the two lines is \( \frac{1}{\sqrt{2}} \)
(b) The shortest distance between the two lines is \( \sqrt{2} \)
(c) Plane containing the line \( L_{2} \) and parallel to line \( L_{1} \) is \( z-x+1=0 \)
(d) Perpendicular distance of origin from plane containing line \( L_{2} \) and parallel to line \( L_{1} \) is \( \frac{1}{\sqrt{2}} \)
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