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Confused! kindly explain, - Three Dimensional Geometry - JEE Main

If the straight lines \frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}\; and\; \frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}\;  intersect at a point, then the integer k is equal to

  • Option 1)

    – 2

  • Option 2)

    – 5

  • Option 3)

    5

  • Option 4)

    2

 
Answers (1)
147 Views

As we learnt in 

Condition for lines to be intersecting (cartesian form) -

Their shortest distance should be 0

Also the condition for coplanar lines

-

 

 If two lines intersect

\Rightarrow \begin{vmatrix} k&2&3 \\ 3&k&2\\ 1&1&-2 \end{vmatrix}= 0

= >2k^{2}+5k-25= 0

= >k= -5,\frac{5}{2}\: \: \: \: \: \: So,\: \: \: k=-5


Option 1)

– 2

Incorrect Option

 

Option 2)

– 5

Correct Option

 

Option 3)

5

Incorrect Option

 

Option 4)

2

Incorrect Option

 

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