Question

Find vectors $\vec{w}, \vec{z}$ in $ℝ^4$ so that $\{\vec u, \vec v, \vec w\}$ is linearly independent but $\{\vec u, \vec v, \vec z\}$ is not

score 3.7k · Answer 1 · 2026-04-15 23:34:59

3.7k

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Find vectors $\vec{w}, \vec{z}$ in $ℝ^4$ so that $\{\vec u, \vec v, \vec w\}$ is linearly independent but $\{\vec u, \vec v, \vec z\}$ is not

Published on 15 Apr 2026 - 23:34

score 167 · Answer 2 · 2026-04-08 17:27:07

167

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Problem on Vectors from "Understanding Pure Mathematics" by Sadler & Thorning

Published on 08 Apr 2026 - 17:27

score 244 · Answer 3 · 2026-04-15 23:49:31

244

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Let $\vec{AA_1} + \vec{BB_1} + \vec{CC_1} = 0$. Prove that the triangle is equilateral.

Published on 15 Apr 2026 - 23:49

score 81 · Answer 4 · 2026-04-14 16:37:41

81

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use of triple scalar product to prove an equality

Published on 14 Apr 2026 - 16:37

score 1.6k · Answer 5 · 2026-04-12 19:11:57

1.6k

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Position Vectors problem

Published on 12 Apr 2026 - 19:11

score 2.3k · Answer 6 · 2026-04-15 19:09:58

2.3k

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What is the meaning of the inner product of a vector and a gradient?

Published on 15 Apr 2026 - 19:09

score 99 · Answer 7 · 2026-04-13 13:23:55

99

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Prove the function $p \mapsto T(p) = (p(1) , p(3))$ is a linear transformation

Published on 13 Apr 2026 - 13:23

score 168 · Answer 8 · 2026-04-14 23:56:31

168

Views

Scale vector of numbers with right proportions

Published on 14 Apr 2026 - 23:56

score 466 · Answer 9 · 2026-04-17 07:51:34

466

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Published on 17 Apr 2026 - 7:51

score 1.5k · Answer 10 · 2026-04-12 09:49:45

1.5k

Views

How to tell where a ray intersects with a plane in 3D space

Published on 12 Apr 2026 - 9:49

score 3.1k · Answer 11 · 2026-04-10 10:10:56

3.1k

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How to explain a vector crossed with its derivative

Published on 10 Apr 2026 - 10:10

score 46 · Answer 12 · 2026-04-16 23:06:27

46

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Line Integral of Vector Field: Inconsistent Answer

Published on 16 Apr 2026 - 23:06

score 61 · Answer 13 · 2026-05-11 07:23:07

61

Views

How to formulate $\sum_{ij} w_{ij}x_i^\top x_j$ in more compressed form?

Published on 11 May 2026 - 7:23

score 195 · Answer 14 · 2026-04-13 13:24:46

195

Views

Find the following (using magnitudes of vectors)

Published on 13 Apr 2026 - 13:24

score 166 · Answer 15 · 2026-04-16 20:49:35

166

Views

Distance of a d dimensional point in a hypercube

Published on 16 Apr 2026 - 20:49

List Question

Find vectors $\vec{w}, \vec{z}$ in $ℝ^4$ so that $\{\vec u, \vec v, \vec w\}$ is linearly independent but $\{\vec u, \vec v, \vec z\}$ is not

Problem on Vectors from "Understanding Pure Mathematics" by Sadler & Thorning

Let $\vec{AA_1} + \vec{BB_1} + \vec{CC_1} = 0$. Prove that the triangle is equilateral.

use of triple scalar product to prove an equality

Position Vectors problem

What is the meaning of the inner product of a vector and a gradient?

Prove the function $p \mapsto T(p) = (p(1) , p(3))$ is a linear transformation

Scale vector of numbers with right proportions

Find a basis for $S^⊥$

How to tell where a ray intersects with a plane in 3D space

How to explain a vector crossed with its derivative

Line Integral of Vector Field: Inconsistent Answer

How to formulate $\sum_{ij} w_{ij}x_i^\top x_j$ in more compressed form?

Find the following (using magnitudes of vectors)

Distance of a d dimensional point in a hypercube

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