Question #216859

Find the vector form of the equation of the plane passing through the point P (1-23) and has normal vector n <3,1, - 1>


1
Expert's answer
2021-07-14T09:43:08-0400

Solution:

Given, point P(1,-2,3), Normal vector = <3,1,-1>

a=(x0,y0,z0)=(1,2,3),N=<A,B,C>=<3,1,1>\overrightarrow a=(x_0,y_0,z_0)=(1,-2,3),\overrightarrow N=<A,B,C>=<3,1,-1>

Vector equation: (ra).N=0(\overrightarrow r-\overrightarrow a).\overrightarrow N=0

(r(i^2j^+3k^)).(3i^+j^k^)=0\Rightarrow (\overrightarrow r-(\hat i-2\hat j+3\hat k)).(3\hat i+\hat j-\hat k)=0

(ri^+2j^3k^).(3i^+j^k^)=0\Rightarrow (\overrightarrow r-\hat i+2\hat j-3\hat k).(3\hat i+\hat j-\hat k)=0


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