Question

Find direction cosines of the normal to the plane `bar"r"*(3hat"i" + 4hat"k")` = 5

Answer 1

Equation of the plane is `bar"r"*(3hat"i" + 4hat"k")` = 5

This is of the form,

`bar"r"*bar"n"` = 5, where `bar"n" = 3hat"i" + 4hat"k"`

Now, `|bar"n"| = sqrt(3^2 + 4^2)`

= `sqrt(9 + 16)`

= 5

The equation `bar"r"*bar"n"` = 5 can be written as

`bar"r"* (bar"n")/|bar"n"| = 5/|bar"n"|`

i.e., `bar"r"*(3/5hat"i" + 4/5hat"k") = 5/5`

= 1

∴ The direction cosines of the normal are `3/5, 0, 4/5`.