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The two lines given by x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are mutually perpendicular when

1. aa' + cc' = -1
2. aa' + cc' = 1
3. a/a' + c/c' = -1
4. a/a' + c/c' = 1

Correct answer: aa' + cc' = -1

Solution

The condition for two lines to be mutually perpendicular in a plane is that the sum of the products of their slopes equals -1. In this case, the slopes are represented by 'a' and 'c' for the first line and 'a'' and 'c'' for the second line, leading to the equation aa' + cc' = -1.

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