Question

Question #af25e

Answer 1

`a=-6`

Explanation:

Since these two lines meet at a right angle that means these two lines are perpendicular.
Two lines are perpendicular if the product of their slopes is -1.

That is two straight lines `color(red)(y=ax+b) and color(blue)(y_1=a_1x+b_1` are perpendicular if `color(green)(a*a_1=-1)`

Here we have:

Equation of the First straight line:
`2y+x+3=0`
`2y=-x-3`
`color(red)(y=-x/2-3/2`
Here the slope is `color(red)(-1/2)`

Equation of the second is:
`3y+ax+2=0`
`3y=-ax-2`
`color(blue)(y=-a/3x-2/3`
Here the slope is `color(blue)(-a/3)`

These two lines are perpendicular that is :
`color(red)(-1/2)*color(blue)(-a/3)=-1`
`a/6=-1`
`a=-6`