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Question
Find the direction cosines of the normal to the plane 12x + 3y – 4z = 65. Also find the non-parametric form of vector equation of a plane and the length of the perpendicular to the plane from the origin
Solution
`vec"d" = 12hat"i" + 3hat"j" - 4hat"k"`
p = 65
`hat"d" = vec"d"/|vec"d"|`
= `(12hat"i" + 3hat"j" - 4hat"k")/sqrt(144 + 9 + 16)`
= `(12hat"i" + 3hat"j" - 4hat"k")/13`
`vec"r"*hat"d"` = p
`vec"r"* ((12hat"i" + 3hat"j" - 4hat"k")/13)`
= `(65/13)`
= 5
Direction cosines of `vec"d"` are `(12/13, 3/13, (-4)/13)` and Length of the ⊥r from the origin = 5 units.
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