When the lines ax + by = 3 and b'x - a'y = 6 area perpendicular to each other what is the relation between a, b, a' and b'

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The slope of a line can be determined by writing it in the slope-intercept form y = m*x + b, where m is the slope.

For ax + by = 3, y = `(3 - ax)/b`

=> y = `-(a/b)*x + 3/b`

The slope is `(-a/b)`

For `b'x - a'y = 6` , y = `(6 + b'x)/(a')`

=> `((b')/(a'))*x + 6/a'`

The slope is `(b')/(a')`

As the two lines are perpendicular to each other the product of the slope is -1.

`(-a/b)*(b')/(a') = -1`

=> `(a*b')/(a'*b) = 1`

One way of expressing the relation between a, b, a' and b' is `(a*b')/(a'*b) = 1`

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