3d vectors qn (1 Viewer)

[Masaken]

Let u, v, and w be vectors in three-dimensional space.
Give a geometric explanation to show that if u + v + w = 0, then the three vectors lie on the same plane.

so i have to prove that u, v, w are coplanar, with the given condition. to start, how do i interpret u + v + w = 0 geometrically? and is this related to saying that they're all linearly independent and whatnot? thanks in advance

 

[tywebb]

There is another geometric explanation too involving the scalar triple product.

 

[5uckerberg]

There is another geometric explanation too involving the scalar triple product.

View attachment 37412

Good attempt however this is beyond the scope of the NSW Mathematics Extension I syllabus.

 

[tywebb]

Is coplanarity in the syllabus? The standard way to do it is with scalar triple product.

 

[5uckerberg]

Is coplanarity in the syllabus? The standard way to do it is with scalar triple product.

Do you notice the fact that you used cross product in vectors. NESA thought, nah students do not have to know this, awakening the wrath of Dr Du when he used the cross product in one of his lessons to roast NESA to pieces.

 

[tywebb]

I just noticed that the Mastering Mathematics Extension 2 book has the following question



So clearly I'm not the only one who thinks scalar triple product is not beyond the capabilities of Extension 2 students.