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Question
Find a parametric form of vector equation of a plane which is at a distance of 7 units from t the origin having 3, – 4, 5 as direction ratios of a normal to it
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Solution
Let `vec"d" = hat"i" - 4hat"j" + 5hat"k"`
p = 7
`vec"d" = vec"d"/|vec"d"|`
= `(3hat"i" - 4hat"j" + 5hat"k")/sqrt(9 + 16 + 25)`
= `(3hat"i" - 4hat"j" + 5hat"k")/sqrt(50)`
= `(3hat"i" - 4hat"j" + 5hat"k")/(5sqrt(2))`
`vec"r"*vec"d"` = p
`vec"r"((3hat"i" - 4hat"j" + 5hat"k")/(5sqrt(2)))` = 7
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