(adsbygoogle = window.adsbygoogle || []).push({}); THE PROBLEM:

The dot product is:

[tex]\overrightarrow{x}\,=\,\left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right][/tex]

[tex]\overrightarrow{y}\,=\,\left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_n \end{array} \right][/tex]

in [tex]\mathbb{R}^n[/tex]:

[tex]\overrightarrow{x}\,\cdot\,\overrightarrow{y}\,=\,x_1\,y_1\,+\,x_2\,y_2\,+\,\ldots\,+\,x_n\,y_n[/tex]

If the scalar [itex]\overrightarrow{x}\,\cdot\,\overrightarrow{y}[/itex] is equal to zero, the vectors are perpendicular.

Find all vectors in [itex]\mathbb{R}^3[/itex] that are perpendicular to

[tex]\left[ \begin{array}{c} 1 \\ 3 \\ -1 \end{array} \right][/tex].

Draw a sketch as well.

MY WORK SO FAR:

[tex]\left[ \begin{array}{c} 1 \\ 3 \\ -1 \end{array} \right]\,\cdot\,\left[ \begin{array}{c} x \\ y \\ z \end{array} \right]\,=\,0[/tex]

[tex]x\,+\,3\,y\,-\,z\,=\,0[/tex]

[tex]z\,=\,x\,+\,3\,y[/tex]

Let s = x and t = y

[tex]z\,=\,s\,+\,3\,t[/tex]

[tex]\left[ \begin{array}{c} 1 \\ 3 \\ -1 \end{array} \right]\,\cdot\,\left[ \begin{array}{c} s \\ t \\ s\,+\,3\,t \end{array} \right]\,=\,0[/tex]

Does the above look right?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Find all vectors in R^3 that are perpendicular to [1; 3; -1]

Loading...

Similar Threads for Find vectors perpendicular | Date |
---|---|

A Find vectors in Orthogonal basis set spanning R4 | Mar 2, 2017 |

I Use Lorentz Force to Find Magnetic Field Components | Aug 8, 2016 |

How to find basis vectors for a+ ax^2+bx^4? | Feb 17, 2016 |

Finding pairs of operator-related vectors | Sep 18, 2015 |

Find the symmetric matrix from eigen vectors | Apr 24, 2013 |

**Physics Forums - The Fusion of Science and Community**