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  • Can someone help me with this, - Three Dimensional Geometry - JEE Main

Lines \frac{x-2}{2}=\frac{y-4}{-2}=\frac{z-0}{4}  and \frac{x-4}{-3}=\frac{y-4}{4}=\frac{z-1}{-2} are

  • Option 1)

    Parallel and coincident lines 

  • Option 2)

    Parallel and non-coincident lines 

  • Option 3)

    intersecting lines 

  • Option 4)

    skew lines 

 

Answers (1)

best_answer

As we have learned

Skew line -

Two straight lines in space which are neither parallel or neither intersecting are called skew lines.

-

 

 here a_{1}=2, b_{1}=-2, c_{1}=4 and a_{2}=-3, b_{2}=4, c_{2}=-2

and \frac{a_{1}}{a_{2}},\frac{b_{1}}{b_{2}},\frac{c_{1}}{c_{2}}  are not all equal so lines are not parallel so (A) and (B) rejected 

For option (C) Let us assume they are intersecting lines 

\thereforePoint on first line \rightarrow(2t+2,4-2t,4t)

Point on second line \rightarrow(4-3t_{1},4+4t_{1},1-2t_{1})

when they intersect :2t+2=4-3t_{1}\Rightarrow 2t+3t_{1}=2\rightarrow(1)

4-2t=4+4t_{1}\Rightarrow2t+4t_{1}=0\rightarrow(2)

and 4t=1-2t_{1}\rightarrow(3)

From (1) and (2)

t_{1}=-2 ,t=4

But it doesnt satisfy (3) so lines dont intersect as well so neither parallel nor intersecting lines 

\therefore Skew lines 

Option (D)


Option 1)

Parallel and coincident lines 

Option 2)

Parallel and non-coincident lines 

Option 3)

intersecting lines 

Option 4)

skew lines 

Posted by

Himanshu

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