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Question

Find the value of p so the line 1x3=7y142p=z32 and 77x3p=y51=6z5 are at right angles.

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Solution

The given equations can be written as
x13=y22p7=z32 and x13p7=y51=z65

If the given lines are at right angles, then,
3(3p7)+2p7(1)+2(5)=0

9p7+2p710=0

11p7=10

11p=70
p=7011

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