# arrow_back Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal

6 views
Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal

We leave it for you to confirm that \begin{aligned} &\mathbf{u}+\mathbf{v}=(-1,5,1,3) \\ &\|\mathbf{u}+\mathbf{v}\|^{2}=36 \\ &\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2}=30+6 \end{aligned} Thus, $\|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2}$
by Platinum
(106,962 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors.
Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors.Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal vectors in $R^{4}$.
Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal vectors in $R^{4}$.Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal vectors in $R^{4}$. ...
If $\mathbf{u}$ and $\mathbf{v}$ are orthogonal vectors in $R^{n}$ with the Euclidean inner product, then prove that $$\|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2}$$If $\mathbf{u}$ and $\mathbf{v}$ are orthogonal vectors in $R^{n}$ with the Euclidean inner product, then prove that $$\|\mathbf{u}+\mathbf{v}\|^{2}= ... close 0 answers 11 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let S=\{\mathbf{i}, \mathbf{j}, \mathbf{k}\} be the set of standard unit vectors in R^{3} . Show that each ordered pair of vectors in S is orthogonal. 1 answer 9 views Let S=\{\mathbf{i}, \mathbf{j}, \mathbf{k}\} be the set of standard unit vectors in R^{3} . Show that each ordered pair of vectors in S is orthogonal.Let S=\{\mathbf{i}, \mathbf{j}, \mathbf{k}\} be the set of standard unit vectors in R^{3} . Show that each ordered pair of vectors in S is ortho ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that two nonzero vectors \mathbf{v}_{1} and \mathbf{v}_{2} in R^{3} are orthogonal if and only if their direction cosines satisfy 0 answers 14 views Show that two nonzero vectors \mathbf{v}_{1} and \mathbf{v}_{2} in R^{3} are orthogonal if and only if their direction cosines satisfyShow that two nonzero vectors \mathbf{v}_{1} and \mathbf{v}_{2} in R^{3} are orthogonal if and only if their direction cosines satisfy$$ \cos \ ...
Let $A$ be an $m \times n$ matrix, and suppose $\vec{v}$ and $\vec{w}$ are orthogonal eigenvectors of $A^{T} A$. Show that $A \vec{v}$ and $A \vec{w}$ are orthogonal.Let $A$ be an $m \times n$ matrix, and suppose $\vec{v}$ and $\vec{w}$ are orthogonal eigenvectors of $A^{T} A$. Show that $A \vec{v}$ and ...