can anyone help me how solve the problem?

Jeff0621

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Feb 22, 2022
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Find a point-normal form and general form of the equation of the plane passing through P and having n as a normal.

P(-1,3,-2); n=(-2,1,-1)
 
I'm unfamiliar with the terms "point-normal" and "general form". There are 2 forms of the equation of a plane I'm familiar with: vector form and scalar form. Suppose [imath]\overrightharpoon{n} = \lang a,b,c\rang[/imath], [imath]P=\lang x,y,z \rang[/imath] and [imath]P_0=\lang x_0,y_0,z_0 \rang[/imath]
Then, in general, the vector form is:
[math]\lang a,b,c \rang\cdot \lang x-x_0,y-y_0,z-z_0\rang=0\\ \boxed{a(x-x_0)+b(y-y_0)+c(z-z_0)=0}[/math]The scalar form:
[math]\boxed{ax+by+cz=ax_0+by_0+cz_0}[/math]Plug the given values into the equations, and you'll have your answer.
 
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