Chapter 11.4, Problem 32E

To determine

To find : the general form of the equation of the plane with the given characteristics.

Answer to Problem 32E

  $x-1=0$

Explanation of Solution

Given information: The plane passes through the point (1,2,3) and is parallel to the $yz$ -plane

Calculation:

We know that x -axis is normal to $yz$ -plane and the required plane is parallel to $yz$ -plane.

Therefore, the direction ratios of normal to the required plane are $\langle 1,0,0\rangle$ .

The equation of plane passing through the point $\left(x_1,y_1,z_1\right)$ is

  $a\left(x-x_1\right)+b\left(y-y_1\right)+c\left(z-z_1\right)=0$

where $\langle a,b,c\rangle$ are direction ratios of normal to the plane.

Therefore, equation of plane passes through the point (1,2,3) and is parallel to the $yz$ -plane is

  $\begin{array}{l}1\left(x-1\right)+0\left(y-2\right)+0\left(z-3\right)=0\\ x-1=0\end{array}$