The given figure shows the path of two balls.
If path followed by the blue ball and the red ball is 2x-5y=4, and 3x-ky=6 respectively.
Determine the value of 'k' for which the path of the balls is parallel.
If the path of both the balls is parallel,
a1a2=b1b2≠c1c2 ...Eq (i)
Given 2x-5y=4, and 3x-ky=6
Here, a1=2, b1=−5, c1=−4
and a2=3, b2=−k, c2=−6
From Eq (i), 23=−5−k≠−4−6
but we can see that 23=−4−6 (i.e. a1a2=c1c2)
so, it is not possible for the balls to have parallel path.