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The two straight lines given by x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are mutually perpendicular if and only if
- aa' + bb' + cc' + 1 = 0
- aa' + bb' + cc' = 0
- (a + a')(b + b') + (c + c') = 0
- aa' + cc' + 1 = 0
Correct answer: aa' + cc' + 1 = 0
Solution
The condition for two lines to be mutually perpendicular in a three-dimensional space involves their directional coefficients. The equation aa' + cc' + 1 = 0 captures the necessary relationship between the slopes of the lines in the x-z plane, ensuring that their angles of intersection are 90 degrees.
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