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Question

Show that the pair of the lines 3x-y=0 and x+3y-3=0is perpendicular.


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Solution

Step 1: Converting the given equations in standard form of a line.

The given lines are 3x-y=0 and x+3y-3=0.

Let, m1,m2 be the slopes of lines 3x-y=0and x+3y-3=0 respectively.

Converting the given line in the form y=mx+c

y=3x and y=-x3+1

Step 2: Showing that lines are perpendicular:

On comparing the above equations with y=mx+c

m1=3 and m2=-13

For any two lines are perpendicular, the product of their slopes must be -1

Now, m1×m2=3×-13

m1×m2=-1

Therefore , the given lines 3x-y=0 and x+3y-3=0 are perpendicular.


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