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MATH / The matrix for projecting onto a certain plane P, which passes through the origin, is given by …

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Answer published by the source. Consult the official source to check your work against its answer.

problem

The matrix for projecting onto a certain plane P,P, which passes through the origin, is given by \[\renewcommand{\arraystretch}{1.5} \begin{pmatrix} \frac{13}{14} & -\frac{1}{7} & \frac{3}{14} \\ -\frac{1}{7} & \frac{5}{7} & \frac{3}{7} \\ \frac{3}{14} & \frac{3}{7} & \frac{5}{14} \end{pmatrix} \renewcommand{\arraystretch}{1}.\]Find the normal vector of plane P.P. Enter your answer in the form $\begin{pmatrix} a \\ b \\ c \end{pmatrix},$ where a,a, b,b, and cc are integers, a>0,a > 0, and gcd(|a|,|b|,|c|)=1.\gcd(|a|,|b|,|c|) = 1.
Plain-text mathematical notation (without MathML)
The matrix for projecting onto a certain plane P, which passes through the origin, is given by
\[\renewcommand{\arraystretch}{1.5} \begin{pmatrix} \frac{13}{14} & -\frac{1}{7} & \frac{3}{14} \\ -\frac{1}{7} & \frac{5}{7} & \frac{3}{7} \\ \frac{3}{14} & \frac{3}{7} & \frac{5}{14} \end{pmatrix} \renewcommand{\arraystretch}{1}.\]Find the normal vector of plane P.  Enter your answer in the form $\begin{pmatrix} a \\ b \\ c \end{pmatrix},$ where a, b, and c are integers, a>0, and gcd(|a|,|b|,|c|)=1.
Original LaTeX notation
The matrix for projecting onto a certain plane $P,$ which passes through the origin, is given by
\[\renewcommand{\arraystretch}{1.5} \begin{pmatrix} \frac{13}{14} & -\frac{1}{7} & \frac{3}{14} \\ -\frac{1}{7} & \frac{5}{7} & \frac{3}{7} \\ \frac{3}{14} & \frac{3}{7} & \frac{5}{14} \end{pmatrix} \renewcommand{\arraystretch}{1}.\]Find the normal vector of plane $P.$  Enter your answer in the form $\begin{pmatrix} a \\ b \\ c \end{pmatrix},$ where $a,$ $b,$ and $c$ are integers, $a > 0,$ and $\gcd(|a|,|b|,|c|) = 1.$

level

Level 5

type

Precalculus

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Source and history

task_id
7e942099-a891-555e-968a-cc5a4b04637b
task_key
precalculus--test--7e942099-a891-555e-968a-cc5a4b04637b
task_revision_id
1
config / split
precalculus / test

Official source

initial import