Question

Unique $u\wedge v$ such that $(u\wedge v)\cdot w = \small\begin{vmatrix} u_1&u_2&u_3 \\ v_1&v_2&v_3 \\ w_1&w_2&w_3 \end{vmatrix}$ for all $w\inℝ^3$

score 163 · Answer 1 · 2021-08-26 04:21:14

163

Views

Unique $u\wedge v$ such that $(u\wedge v)\cdot w = \small\begin{vmatrix} u_1&u_2&u_3 \\ v_1&v_2&v_3 \\ w_1&w_2&w_3 \end{vmatrix}$ for all $w\inℝ^3$

Published on 26 Aug 2021 - 4:21

score 735 · Answer 2 · 2021-08-28 01:02:12

735

Views

Proof that the determinant of a $3 \times 3$ matrix is the volume of the parallelepiped spanned by the columns

Published on 28 Aug 2021 - 1:02

score 142 · Answer 3 · 2021-09-11 03:02:11

142

Views

Given $U \times V=\langle -4,-2,-1 \rangle$, find $(U-3V) \times (U+2V)$

Published on 11 Sep 2021 - 3:02

score 122 · Answer 4 · 2026-03-25 16:03:16

122

Views

Clarification of Wikipedia's index formula for cross product

Published on 25 Mar 2026 - 16:03

score 36 · Answer 5 · 2021-09-28 00:22:33

36

Views

Why are cross products in different coordinates different?

Published on 28 Sep 2021 - 0:22

score 493 · Answer 6 · 2021-10-11 10:45:05

493

Views

Why is a vector equal to the sum of its projection on other vectors?

Published on 11 Oct 2021 - 10:45

score 150 · Answer 7 · 2026-02-23 13:45:55

150

Views

Geometric proof of the Cross Product magnitude (without using sine and additional assumptions)

Published on 23 Feb 2026 - 13:45

score 52 · Answer 8 · 2021-10-12 17:00:23

52

Views

How to use projection of vectors in order to compute length of a cross product?

Published on 12 Oct 2021 - 17:00

score 914 · Answer 9 · 2021-10-14 17:50:16

914

Views

Determine the volume of the parallelepiped spanned by the given vectors?

Published on 14 Oct 2021 - 17:50

score 1k · Answer 10 · 2021-10-15 08:42:55

1k

Views

Finding $\vec b$ from $\vec a \times \vec b$ , $\vec a$ and $\alpha=\angle(\vec a;\vec b)$ using only vector algebra.

Published on 15 Oct 2021 - 8:42

score 63 · Answer 11 · 2021-10-15 16:36:08

63

Views

Determine the area of the triangle PQR and the volume of the tetrahedron PQRS?

Published on 15 Oct 2021 - 16:36

score 69 · Answer 12 · 2021-10-30 12:39:42

69

Views

Difference Moment with Cross Product and with F x r

Published on 30 Oct 2021 - 12:39

score 118 · Answer 13 · 2021-11-09 19:29:44

118

Views

Simplifying an expression of dot product and cross product (Vector Valued Functions)

Published on 09 Nov 2021 - 19:29

score 42 · Answer 14 · 2021-11-13 07:00:26

42

Views

triple cross product (for beginner)

Published on 13 Nov 2021 - 7:00

score 130 · Answer 15 · 2021-11-17 08:05:35

130

Views

Given $v_1, \ldots , v_{n-1}\in \mathbb{R}^n$, show there is a unique $v\in \mathbb{R}^n$ such that $\det (u \ v_1 \ldots v_{n-1})=u\cdot v$.

Published on 17 Nov 2021 - 8:05

List Question

Unique $u\wedge v$ such that $(u\wedge v)\cdot w = \small\begin{vmatrix} u_1&u_2&u_3 \\ v_1&v_2&v_3 \\ w_1&w_2&w_3 \end{vmatrix}$ for all $w\inℝ^3$

Proof that the determinant of a $3 \times 3$ matrix is the volume of the parallelepiped spanned by the columns

Given $U \times V=\langle -4,-2,-1 \rangle$, find $(U-3V) \times (U+2V)$

Clarification of Wikipedia's index formula for cross product

Why are cross products in different coordinates different?

Why is a vector equal to the sum of its projection on other vectors?

Geometric proof of the Cross Product magnitude (without using sine and additional assumptions)

How to use projection of vectors in order to compute length of a cross product?

Determine the volume of the parallelepiped spanned by the given vectors?

Finding $\vec b$ from $\vec a \times \vec b$ , $\vec a$ and $\alpha=\angle(\vec a;\vec b)$ using only vector algebra.

Determine the area of the triangle PQR and the volume of the tetrahedron PQRS?

Difference Moment with Cross Product and with F x r

Simplifying an expression of dot product and cross product (Vector Valued Functions)

triple cross product (for beginner)

Given $v_1, \ldots , v_{n-1}\in \mathbb{R}^n$, show there is a unique $v\in \mathbb{R}^n$ such that $\det (u \ v_1 \ldots v_{n-1})=u\cdot v$.

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