All Questions
6
questions
3
votes
1
answer
711
views
Matrix-vector multiplication/cross product problem
How can I generally solve equations of the form $\mathbf{A} \mathbf{w} =
\begin{pmatrix} x \\ y \\ z \end{pmatrix}
\times \mathbf{w}$ for the matrix $\mathbf{A},$ where $\mathbf{w}$ can be any vector? ...
- 47
3
votes
3
answers
966
views
How can I find the cross product of an inner sum and difference between two vectors?
The problem is as follows:
The figure from below shows vectors $\vec{A}$ and $\vec{B}$. It is known that $A=B=3$. Find $\vec{E}=(\vec{A}+\vec{B})\times(\vec{A}-\vec{B})$
The alternatives are:
$\...
- 4,185
1
vote
0
answers
47
views
Solving vector equation employing products.
If $$\vec{a}\times(\vec{b}\times\vec{c})+(\vec{a}\cdot\vec{b})\vec{b}=(4-2\lambda-\sin\alpha)\vec{b}+(\lambda^2-1)\vec{c}$$ and $(\vec{c}\cdot\vec{c})\vec{a}=\vec{c}$ where $\vec{b},\vec{c}$ are ...
- 3,381
2
votes
3
answers
287
views
Collinearity when $\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a} = \mathbf{0}$
Let $\mathbf{a} = \begin{pmatrix}x_a\\y_a\\z_a\end{pmatrix}$, $\mathbf{b} = \begin{pmatrix}x_b\\y_b\\z_b\end{pmatrix}$, and $\mathbf{c} = \begin{pmatrix}x_c\\y_c\\z_c\end{pmatrix}$.
Show that $(x_a,...
- 4,581
2
votes
2
answers
224
views
Trying to show $|\overrightarrow{a}\times\overrightarrow{b}|^2=|\overrightarrow{a}|^2|\overrightarrow{b}|^2-(\overrightarrow{a}⋅\overrightarrow{b})^2$
If $\overrightarrow{a} = \langle a_1, a_2, a_3 \rangle$ and $\overrightarrow{b} = \langle b_1, b_2, b_3 \rangle$, then the cross product of $\overrightarrow{a}$ and $\overrightarrow{b}$ is the vector
$...
- 608
3
votes
2
answers
74
views
Finding $P$ knowing $\overrightarrow{PQ}×\overrightarrow{b}$, $\overrightarrow{PQ}⋅\overrightarrow{c}$, $\overrightarrow{b}$, and $\overrightarrow{c}$
Let $Q$ be the point $(1,2,3)$, let $\overrightarrow{b} = \langle -1, 0, 1\rangle$, and let $\overrightarrow{c} = \langle 2, 1, 5\rangle$. It is known that $\overrightarrow{PQ} \times \overrightarrow{...
- 608