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Mathematics-Online problems:

Interactive Problem 120: Vectors Represented With Respect to an Orthonormal Basis

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Show that the vectors

$\displaystyle \vec{u}= \begin{pmatrix}6 \\ -3 \\ 2 \end{pmatrix}, \quad \vec{v... ...\\ 3 \end{pmatrix}, \quad \vec{w}= \begin{pmatrix}3 \\ 2 \\ -6 \end{pmatrix} $

are mutually orthogonal. Do they form a left-handed or a right-handed system?

Keine Angabe ,     left-handed ,      right-handed .

Calculate the magnitudes $ \vert\vec{u}\vert$, $ \vert\vec{v}\vert$, $ \vert\vec{w}\vert$ and find $ \alpha,\beta,\gamma\in \mathbb{R}$ so that

$\displaystyle \frac{\alpha}{\vert\vec{u}\vert}\,\vec{u} + \frac{\beta}{\vert\v... ...vert\vec{w}\vert}\,\vec{w} = \begin{pmatrix}14 \\ -7 \\ 0 \end{pmatrix} \; . $

Solution:

Magnitudes:
$ \vert\vec{u}\vert=$,      $ \vert\vec{v}\vert=$,      $ \vert\vec{w}\vert=$.

Parameter:
$ \alpha=$,     $ \beta=$,     $ \gamma=$.
   

see also:

  automatically generated: 8/11/2017