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Question
Solve the following :
The foot of the perpendicular drawn from the origin to a plane is M(1, 2, 0). Find the vector equation of the plane.
Solution
The vector equation of the plane passing through A`(bara)` and perpendicular to `bar"n" "is" bar"r".bar"n" = bar"a".bar"n"`.
M(1, 2, 0) is the foot of the perpendicular drawn from origin to the plane. Then the plane is passing through M and is perpendicular to OM.
If `bar"m"` is the position vector of M, then `bar"m" = hat"i"`.
Normal to the plane is
`bar"n" = bar"OM" = hat"i"`
`bar"m".bar"n" = hat"i".hat"i"` = 5
∴ the vector equation of the required plane is
`bar"r".(hat"i" + 2hat"j")` = 5.
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