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Question
Reduce the equation `bar"r"*(3hat"i" + 4hat"j" + 12hat"k")` = 8 to normal form
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Solution
Equation of plane is `bar"r"*(3hat"i" + 4hat"j" + 12hat"k")` = 8
This is of the form,
`bar"r"*bar"n"` = 8, where `bar"n" = 3hat"i" + 4hat"j" + 12hat"k"`
Now, `|bar"n"| = sqrt(3^2 + 4^2 + 12^2)`
= `sqrt(9 + 16 + 144)`
= 13
The equation `bar"r"*bar"n"` = 8 can be written as
`bar"r"* (bar"n")/|bar"n"| = 8/|bar"n"|`
i.e., `bar"r"*(3/13hat"i" + 4/13hat"j" + 12/13hat"k") = 8/13`,
which is the normal form of the plane.
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