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Find the equation of the plane passing through \((1,2,3)\) and \((1,-3,2)\) and parallel to the \(z\)-axis.
- Parallel Planes
Parallel planes are planes in the same three-dimensional...
- Parallel Planes
27 Ιαν 2022 · A good way to prepare for sketching a plane is to find the intersection points of the plane with the \(x\)-, \(y\)- and \(z\)-axes, just as you are used to doing when sketching lines in the \(xy\)-plane. For example, any point on the \(x\) axis must be of the form \((x,0,0)\text{.}\) For \((x,0,0)\) to also be on \(P\) we need \(x=\frac{12}{4 ...
10 Νοε 2020 · Euclidean space has three mutually perpendicular coordinate axes (\(x, y\) and \(z\)), and three mutually perpendicular coordinate planes\index{plane!coordinate}: the \(xy\)-plane, \(yz\)-plane and \(xz\)-plane (Figure \(\PageIndex{2}\) ).
Parallel planes are planes in the same three-dimensional space that never meet. If we let two planes \( \alpha\) and \( \beta \) be as follows: \[ \begin{align} \alpha : a_{1}x+b_{1}y+c_{1}z+d_{1} &= 0 \\ \beta : a_{2}x+b_{2}y+c_{2}z+d_{2} &= 0, \end{align} \]
Suppose three planes intersect at a point O such that these three planes are mutually perpendicular to each other, as shown in the below figure. These three planes intersect along the lines X′OX, Y′OY and Z′OZ, and are respectively called the x, y and z-axes.
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system[8]) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.
20 Μαρ 2011 · For three points to determine a unique plane, you need the three points to not be collinear (not lie on the same line). You will find this when you compute the vector $\mathbf{n}$. If $\mathbf{n}=(0,0,0)$, then $\mathbf{v}_1$ and $\mathbf{v}_2$ are parallel, so that means that the three points are collinear and don't determine a unique plane.
