The number of real values of k for which the lines
x-2y+3=0
kx+3y+1=0
4x-ky+2=0
are concurrent is..?

Question

The  number of real values of k for which the lines 
x-2y+3=0
kx+3y+1=0
4x-ky+2=0
are concurrent is..?

amistre64 · Answer

concurrent means ... the same?

dls · Answer

In geometry, three or more lines in a plane are said to be concurrent if they intersect at a single point.

amistre64 · Answer

ahhh

amistre64 · Answer

then we want independant vectors ... ie, determinant = 0

dls · Answer

thats what we did prev ques ryt

amistre64 · Answer

yep, and the easy way is always the best way :)

shubhamsrg · Answer

you may also, alternatively , find values of x and y in terms of k from any 2 eqns and plug it into 3rd to find real values of k satisfying it..

anyways,,still, determinant method is more easy..

dls · Answer

yeah former is lengthy

amistre64 · Answer

- (36-k-4k )
1 -2  3  1 -2
k   3  1  k   3
4 -k  2  4  -k
       + (6-8-3k^2)

(6-8-3k^2)- (36-k-4k )= 0

amistre64 · Answer

well, there are no real solutions if i did the correctly