Practicing Success
The lines with direction cosines 12/17, -3/17, -4/17 and 4/17, 12/17, 3/17 are- |
Perpendicular Non-perpendicular May or may not be perpendicular None of these |
Perpendicular |
The lines with direction cosines l1, m1, n1 and l2, m2,n2 are perpendicular to each other if l1.l2+ m1.m2+ n1.n2 = 0 We have the lines with direction cosines 12/17, -3/17, -4/17 and 4/17, 12/17, 3/17 so l1.l2+ m1.m2+ n1.n2 = (12/17).(4/17) + (-3/17).(12/17) + (-4/17).(3/17) ⇒ l1.l2+ m1.m2+ n1.n2 = (48/289) -(36/289) - (12/289) ⇒ l1.l2+ m1.m2+ n1.n2 = 0 Therefore the line are perpendicular.
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