# arrow_back 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

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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 $$\cos \alpha_{1} \cos \alpha_{2}+\cos \beta_{1} \cos \beta_{2}+\cos \gamma_{1} \cos \gamma_{2}=0$$

Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y)$ that satisfy the stated condition.Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y) ... close 1 answer 5 views If$\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 5 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$\mathbf{v}=(a, b)$and$\mathbf{w}=(-b, a)$are orthogonal vectors. 0 answers 4 views 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 If$\|\mathbf{v}\|=2$and$\|\mathbf{w}\|=3$, what are the largest and smallest values possible for$\|\mathbf{v}-\mathbf{w}\|$? Give a geometric explanation of your results. 0 answers 12 views If$\|\mathbf{v}\|=2$and$\|\mathbf{w}\|=3$, what are the largest and smallest values possible for$\|\mathbf{v}-\mathbf{w}\|$? Give a geometric explanation of your results.If$\|\mathbf{v}\|=2$and$\|\mathbf{w}\|=3$, what are the largest and smallest values possible for$\|\mathbf{v}-\mathbf{w}\|$? Give a geometric exp ... close 0 answers 101 views Let$\mathbf{u}$be a vector in$R^{100}$whose$i$th component is$i$, and let$\mathbf{v}$be the vector in$R^{100}$whose$i$th component is$1 /(i+1)$. Find the dot product of$\mathbf{u}$and$\mathbf{v}$.Let$\mathbf{u}$be a vector in$R^{100}$whose$i$th component is$i$, and let$\mathbf{v}$be the vector in$R^{100}$whose$i$th component is$1 ...