Notes

 

Practice Problems

\(\textbf{1)}\) Does the point \((4,2,7)\) lie on the plane \(2x+3y-2z=0\)?

Show Answer

Yes, the point does lie on the plane.

Show Work

\(2(4)+3(2)-2(7)=0\)

 

\(\textbf{2)}\) Does the point \((1,2,3)\) lie on the plane \(x-2y+z=0\)?

Show Answer

Yes, the point does lie on the plane.

Show Work

\((1)-2(2)+(3)=0\)

 

\(\textbf{3)}\) Does the point \((0,3,1)\) lie on the plane \(5x+2y=0\)?

Show Answer

No, the point does not lie on the plane.

Show Work

\(5(0)+2(3)=6\)

 

\(\textbf{4)}\) Does the point \((5,-4,-8)\) lie on the plane \(x-y+2z=0\)?

Show Answer

No, the point does not lie on the plane.

Show Work

\((5)-(-4)+2(-8)=-7\)

 

 

See Related Pages\(\)

\(\bullet\text{ Displacement Vectors}\)
\(\,\,\,\,\,\,\,\,(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}…\)

\(\bullet\text{ Magnitude, Direction, and Unit Vectors}\)
\(\,\,\,\,\,\,\,\,|\vec{u}|=\sqrt{a^2+b^2}…\)

\(\bullet\text{ Dot Product}\)
\(\,\,\,\,\,\,\,\,a \cdot b=x_1 x_2+ y_1 y_2…\)

\(\bullet\text{ Parallel and Perpendicular Vectors}\)
\(\,\,\,\,\,\,\,\,⟨8,2⟩ \text{ and } ⟨−4,−1⟩…\)

\(\bullet\text{ Scalar and Vector Projections}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{a \cdot b}{|b|^2} \, \vec{b}…\)

\(\bullet\text{ Cross Product}\)
\(\,\,\,\,\,\,\,\,\)\(…\)

\(\bullet\text{ Equation of a Plane}\)
\(\,\,\,\,\,\,\,\,Ax+By+Cz=D…\)

 

In Summary

“Is this point on this plane?” is a question that is often asked in geometry, specifically in the study of three-dimensional space. It refers to determining whether a specific point in space lies on a particular plane, or if the coordinates of the point satisfy the equation of the plane.