Finding the scalar equation of a plane
Formula for the scalar equation of a plane
To find the scalar equation of a plane, we’ll use the formula
???a(x-x_0)+b(y-y_0)+c(z-z_0)=0???
where ???P_0(x_0,y_0,z_0)??? is a given point and ???v=\langle a,b,c\rangle??? is the normal vector to the plane. The vector may also be in the format ???v=ai+bj+ck???.
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Scalar equation for a plane, given a vector and a point
Example
Find the scalar equation of the plane.
???P(1,4,-8)???
???\langle3,6,2\rangle???
Plugging the given point and the given vector into our formula, we get
???3(x-1)+6(y-4)+2\left[z-(-8)\right]=0???
???3(x-1)+6(y-4)+2(z+8)=0???
???3x-3+6y-24+2z+16=0???
???3x+6y+2z=11???
The scalar equation of the plane is given by ???3x+6y+2z=11???.
IF we have a vector and a point, we can find the scalar equation of a plane.
