Questions tagged [vectors]
Use this tag for questions and problems involving vectors, e.g., in an Euclidean plane or space. More abstract questions, might better be tagged vector-spaces, linear-algebra, etc.
12,784 questions
-1 votes
1 answer
48 views
Rotating a unit vector to another vector using two consecutive axes
Given a unit vector $u$ and another unit vector $v$, I want to rotate $u$ into $v$ in two stages. In the first stage, I rotate $u$ about a given axis $a_1$ (by an unknown angle) to produce a vector $...
- 126
1 vote
3 answers
56 views
Cartesian equation of X axis [closed]
In my school module it is written that the cartesian equation of $x$ axis is $$ \frac{x}{1}=\frac{y}{0}=\frac{z}{0} $$ Isn't dividing by zero not allowed? How have they written this equation
- 13
2 votes
2 answers
111 views
Rotate vector within plane by given angle
Let two 3D unit vectors $V, V'$ be given. Derive vector $W$ created by clockwise rotating $V'$ by angle $\theta'$ around the origin within the plane with normal proportional to $V \times V'$. I tried ...
- 357
0 votes
1 answer
31 views
Vector tangent to meridian
Let there be two different points $ \vec{p_1}, \vec{p_2}$ on a unit sphere. I need to get unit vector $\vec{t}$ at the point $\vec{p_1}$ tangent to the meridian (big circle) connecting these points. ...
- 897
0 votes
1 answer
52 views
Simple Algebraic Derivation of the Cross Product [duplicate]
I'm looking for a simple algebraic derivation of the cross product formula: $\vec{a} \times \vec{b} = \|\vec{a}\| \|\vec{b}\| \sin(\theta) \vec{n}$. I need the derivation to be simple, understandable ...
- 123
0 votes
1 answer
84 views
Bearing angle of great circular arc between Ottawa Canada, and Sarajevo, Bosnia
I have this problem that I have been working on today. I want to calculate the local direction of the great circle connecting Ottawa, Canada, and Sarajevo, Bosnia. I assume Earth is perfectly ...
user1709783
0 votes
1 answer
56 views
Show that $pr_d(\overrightarrow{u}+\overrightarrow{v}) = pr_d\overrightarrow{u} + pr_d\overrightarrow{v}$
On a plane, give a line $d$ and the vectors $\overrightarrow{u}, \overrightarrow{v}\ne\overrightarrow{0}$ such that $\overrightarrow{u},\overrightarrow{v}$ are not perpendicular to the line $d$. Let $...
- 895
-2 votes
2 answers
81 views
I don't believe me, $\overrightarrow{Marc}(1.80\ m, 71\ kg, 56\ y.o.)$ I'm a vector of $\mathbb{R^3}$. But of $\mathbb{R^{+3}}$ or better. Am I right?
My beliefs: At school, I've seen all the time definition of vectors in $\mathbb{R^n}$. I've understood that if some are defined in $\mathbb{R^3}$ it means that: they all have three components all of ...
- 269
0 votes
1 answer
85 views
Why is the $z$ partial derivative of $z = f(x,y)$ equals to $-1$?
We know that a vector $(a,b,c)$ is perpendicular to a plane iff the equation of the plane is equivalent to $$ax+by+cz+d=0$$ We also hear that "the gradient of $f$ is perpendicular to its tangent ...
- 2,080
0 votes
1 answer
85 views
A technical question regarding forward passes [closed]
I am a mathematician writing an article on rugby forward passes and am looking for a little help with a definition. Issue is this: If I am standing on the 25 metre line and pass the ball laterally ...
- 61
0 votes
1 answer
86 views
Question on a collinear configuration on quadrilateral
I faced the following problem when fooling around with quadrilaterals. Let $ABCD$ be a convex quadrilateral. On the edge AB, CD, pick E, F such that $\dfrac{EB}{EA} =\dfrac{FC}{FD}$. Let $M, P, N$ be ...
- 561
0 votes
0 answers
75 views
$\vec{C} = \vec{A} - \vec{B}$. Scalar product: $\hat{\vec{A},\vec{B}} = 63.4$°, $\hat{\vec{A},\vec{C}}$ = 90° but $\hat{\vec{B},\vec{C}} = 153$°
From a $\vec{A}$ and a $\vec{B}$ vector, I'm trying to extract all the useful values and indications that can be gained through the calculation of their scalar product. And I'm impressed that they are ...
- 269
-1 votes
1 answer
63 views
Calculate the angle between 3-dimensional lines [closed]
I have two 3-dimensional line segments ($a$ and $b$). The end point of line segment $a$ is the starting point of $b$. Given are their lengths when projected on a horizontal plane ($d_a$ and $d_b$) as ...
- 99
1 vote
0 answers
43 views
Was a vector "an arrow with magnitude and direction" at the beginning, or did the abstraction happen early on? [migrated]
Many people seem to think that the picture of a vector that introductory physics gives (as an arrow with magnitude and direction) came before the more modern, abstract notion that we have today. It is ...
- 335
1 vote
4 answers
288 views
I cannot verify $\vec{A}\cdot\vec{B} = (A_x\vec{i} + A_y\vec{j}+ A_z\vec{k})\cdot(B_x\vec{i} + B_y\vec{j}+ B_z\vec{k})$
According to my book, for a scalar product, this relation is true: $$\vec{A}\cdot\vec{B} = (A_x\vec{i} + A_y\vec{j}+ A_z\vec{k})\cdot(B_x\vec{i} + B_y\vec{j}+ B_z\vec{k})$$ But I cannot verify it on ...
- 269