Questions tagged [vectors]

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7 votes
7 answers

Creative problems in 2D vector geometry

What are some "interesting" and creative problems or exercises on specifically 2-dimensional vector geometry that a high school student might find compelling to solve? The class' current ...
19 votes
11 answers

Why do we still teach the determinant formula for cross product? And is it as bad as I think it is?

The cross product is an important vector operation in in any serious multivariable calculus course. In most textbooks that I'm aware of, right after the definition, we always introduce the ...
2 votes
0 answers

Teaching linear algebra, wacom tablet display of coordinate system, eigenvectors, markov chains

I am teaching linear algebra as part of an information retrieval course, which now occurs online. I have a Wacom tablet and free drawing software, sketchBook for artists, so can draw circles ellipses ...
16 votes
4 answers

What are some of the open problems that can be suitably introduced in a calculus course?

I feel it may be a good idea to introduce some related open problems in a calculus course. Surely I am not expecting my students to solve any one of them, though I cannot say it is absolutely ...
7 votes
5 answers

How do you plausibly explain that the geometric and the coordinate expressions for the scalar product are equivalent?

The standard scalar product on $\mathbb{R}^3$ is defined via $$\vec a\cdot\vec b := a_1b_1+a_2b_2+a_3b_3$$ On the other hand, it can be expressed in a more geometrical way through the lengths of the ...
10 votes
2 answers

3D vectors with 3D glasses?

I am going to teach 3D vectors soon to my A-level students. Last time I taught it a lot of them struggled to visualise the angle between two vectors in 3D space. I had an idea that I could get them ...
7 votes
3 answers

Why is it difficult to freely change between points and vectors?

I have noticed working with bright undergraduates that it is not uncommon for them to have difficulty easily converting between a point—say, a point $p$ on a surface $S \subset \mathbb{R}^3$&...
6 votes
1 answer

Difficulty in teaching the coordinates of a vector with respect to a basis $\{v_1,v_2,\ldots,v_n\}$

Let $V$ be a finite dimensional vector space and let $B=\{v_1,v_2,\cdots,v_n\}$ be a basis of $V$. If a vector $v$ can be written as $$v=a_1v_1+a_2v_2+\cdots+a_nv_n,$$ we call $(a_1,a_2,\cdots,a_n)$...
5 votes
2 answers

Presenting ways to find a resultant force

To begin with I am working in a high school classroom where the students are working on the applications of vectors. The beginning of the lesson is about calculating direction and magnitude of vectors ...
2 votes
2 answers

Line Integral Motivation

Is there a case to be made that the topic of line integrals should only involve vector fields? My colleagues and our textbook take the position that line integrals should only be taught from a vector ...