Question

the line 2x+y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent
a.for all
b.for a=4
c.(-1to3)
d.a>0

Answer 1

this answer may satisfies u

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Answer 2

answer : option (a) for all

it is given that,

2x + y - 1 = 0

ax + 3y - 3 = 0

3x + 2y - 2 = 0 are concurrent.

so, determinant of coefficients and constants of all these three straight lines = 0

I mean, $\left|\begin{array}{ccc}2&1&-1\\a&2&-3\\3&2&-2\end{array}\right|=0$

⇒2(3 × -2 - 2 × -3) - 1(a × -2 - 3 × -3) -1(a × 2 - 3 × 3) = 0

⇒2(-6 + 6) - (-2a + 9) -(2a - 9) = 0

⇒0 + 2a - 9 - 2a + 9 = 0

⇒0 = 0

for all real value of a, given lines will be concurrent.

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