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  • Find K , So that the staright lines  <img alt="L_1 : 3x-y +2 = 0 \\ L_2 : x+y -4 = 0 \\ L_3 : kx -y +1 =0" src="https://learn.careers360.com/latex-image/?L_1%20%3A%203x-y%20&plus

Find K , So that the staright lines 

L_1 : 3x-y +2 = 0 \\ L_2 : x+y -4 = 0 \\ L_3 : kx -y +1 =0 are concurrent 

 

Option: 1

3 


Option: 2

4 


Option: 3

-3 


Option: 4

5


Answers (1)

best_answer

As we have learned

Condition of concurrency -

\begin{vmatrix} a_{1} & b_{1} & c_{1}\\ a_{2}& b_{2} &c_{2} \\ a_{3} & b_{3} &c_{3} \end{vmatrix}=0
 

- wherein

Three lines    a_{1}x+b_{1}y+c_{1}=0 , a_{2}x+b_{2}y+c_{2}=0  and a_{3}x+b_{3}y+c_{3}=0  are concurrent.

 

 \begin{vmatrix} 3 & -1&2 \\ 1 & 1& -4\\ k &-1 &1 \end{vmatrix} = 0

 

3 (1-4) +1 (1+4k )+ 2 (-1-k) = 0 

-9 +(1+4k)-2 (k+1) = 0 

2k=10

k = 5

Posted by

Suraj Bhandari

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