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Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?

1/9
9
-9
-1/9

Pls answer​

User Alexpfx
by
8.4k points

1 Answer

4 votes

Answer:


\boxed{\sf a = 9 }

Explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,


\sf\longrightarrow 3x - 2y +7=0


\sf\longrightarrow 6x +ay -18 = 0

Step 1 : Convert the equations in slope intercept form of the line .


\sf\longrightarrow y = (3x)/(2) +( 7 )/(2)

and ,


\sf\longrightarrow y = -(6x )/(a)+(18)/(a)

Step 2: Find the slope of the lines :-

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,


\sf\longrightarrow Slope_1 = (3)/(2)

And the slope of the second line is ,


\sf\longrightarrow Slope_2 =(-6)/(a)

Step 3: Multiply the slopes :-


\sf\longrightarrow (3)/(2)* (-6)/(a)= -1

Multiply ,


\sf\longrightarrow (-9)/(a)= -1

Multiply both sides by a ,


\sf\longrightarrow (-1)a = -9

Divide both sides by -1 ,


\sf\longrightarrow \boxed{\blue{\sf a = 9 }}

Hence the value of a is 9 .

User Dumkar
by
8.5k points

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