Finding coordinates given 3-dimensional vectors

[mystmyst]

Homework Statement

<br /> \begin{align*}<br /> \vec{u} = 2 \hat{x} - 3 \hat{y} + \hat{z}<br /> \vec{v} = \hat{x} - \hat{y} - \hat{z}<br /> \end{align*}<br />

Given a parallelogram that's vertex is at the origin (0,0,0) and is created by two vectors u and v:

a) find where the fourth vertex is of the parallelogram
b) find the length of the two diagonals

The Attempt at a Solution

a) since it's a parallelogram, the fourth point is at u + v = 3 \hat{x} - 4 \hat{y} ------- I'm not sure if the answer is supposed to be in this form or in form (3,-4,0)

b) I'm not sure about this one. By length, do they mean distance? Should I use the distance formula between two points? Or do they possibly mean vector addition/subtraction?

Thanks!

 

[Karlx]

Hi mysmyst.

a) The vector u+v points to the fourth vertex, whose coordinates are (3,-4,0)

b) You may calculate the vectors that follow the diagonals, from u and v, and then calculate their modules.

 

[mystmyst]

the big diagonal is obviously u+v. but is the little diagonal u-v or v-u? and how do I tell which it is in general?

Thanks!

 

[Karlx]

The little diagonal is (v-u) and also (u-v). It doesn't matter. It depends on which sense you see it.

 

[mystmyst]

o. that was silly (:

Thanks!

is there a thanks button?