# arrow_back Let $\mathbf{u}$ and $\mathbf{v}$ be nonzero vectors in 2 - or 3 -space, and let $k=\|\mathbf{u}\|$ and $l=\|\mathbf{v}\|$. Prove that the vector $\mathbf{w}=l \mathbf{u}+k \mathbf{v}$ bisects the angle between $\mathbf{u}$ and $\mathbf{v}$.

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Let $\mathbf{u}$ and $\mathbf{v}$ be nonzero vectors in 2 - or 3 -space, and let $k=\|\mathbf{u}\|$ and $l=\|\mathbf{v}\|$.

Prove that the vector $\mathbf{w}=l \mathbf{u}+k \mathbf{v}$ bisects the angle between $\mathbf{u}$ and $\mathbf{v}$.

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 $$\|\mathbf{u}+\mathbf{v}\|^{2}= ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Proof or counterexample. Here $v, w, z$ are vectors in a real inner product space $H$. 0 answers 5 views Proof or counterexample. Here $v, w, z$ are vectors in a real inner product space $H$.Proof or counterexample. Here $v, w, z$ are vectors in a real inner product space $H$. a) Let $v, w, z$ be vectors in a real inner product space ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find all vectors in the plane (through the origin) spanned by $\mathbf{V}=(1,1-2)$ and $\mathbf{W}=(-1,1,1)$ that are perpendicular to the vector $\mathbf{Z}=(2,1,2)$. 0 answers 2 views Find all vectors in the plane (through the origin) spanned by $\mathbf{V}=(1,1-2)$ and $\mathbf{W}=(-1,1,1)$ that are perpendicular to the vector $\mathbf{Z}=(2,1,2)$.Find all vectors in the plane (through the origin) spanned by $\mathbf{V}=(1,1-2)$ and $\mathbf{W}=(-1,1,1)$ that are perpendicular to the vector ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that two nonzero vectors \mathbf{v}_{1} and \mathbf{v}_{2} in R^{3} are orthogonal if and only if their direction cosines satisfy 0 answers 10 views Show that two nonzero vectors \mathbf{v}_{1} and \mathbf{v}_{2} in R^{3} are orthogonal if and only if their direction cosines satisfyShow that two nonzero vectors \mathbf{v}_{1} and \mathbf{v}_{2} in R^{3} are orthogonal if and only if their direction cosines satisfy$$ \cos \ ...
Let $\mathcal{P}_{k}$ be the space of polynomials of degree at most $k$ and define the linear map $L: \mathcal{P}_{k} \rightarrow \mathcal{P}_{k+1}$ by $L p:=p^{\prime \prime}(x)+x p(x) .$Let $\mathcal{P}_{k}$ be the space of polynomials of degree at most $k$ and define the linear map $L: \mathcal{P}_{k} \rightarrow \mathcal{P}_{k+ ... close 0 answers 46 views 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 Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \(U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars.
Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars.Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars. a) (Pythagoras) Show that \(\|Z\|^{2}=a^{2}\|U\|^{2}+b ...