# Thread: [SOLVED] Determining if one vector is perpendicular to another.

1. ## [SOLVED] Determining if one vector is perpendicular to another.

If the vectors u, v and w in R3 are given by:
....[ 1]....[-2]....[-2]
U = [-1] V =[ 3] W =[ 1]
....[ 3]....[ 1]....[ 1]

determine which (if any) of the following statements are true:
(i) u is perpendicular to v.
(ii) u is perpendicular to w.
(iii) v is perpendicular to w.

This is a sample question from an exam I had recently. Im not to interested in the answer. More interested in the technique and formulas used.
Apologies for the periods.

Any help is greatly appreciated.

2. Originally Posted by crakapete
If the vectors u, v and w in R3 are given by:
....[ 1]....[-2]....[-2]
U = [-1] V =[ 3] W =[ 1]
....[ 3]....[ 1]....[ 1]

determine which (if any) of the following statements are true:
(i) u is perpendicular to v.
(ii) u is perpendicular to w.
(iii) v is perpendicular to w.

This is a sample question from an exam I had recently. Im not to interested in the answer. More interested in the technique and formulas used.
Apologies for the periods.

Any help is greatly appreciated.

Just dot multi8ply the vectors involved: if and only if you get zero the vectors are perpendicular...yes, as easy and simple as that!
For example, u isn't perp. to w ...

Tonio

3. $\displaystyle <\mathbf{x},\mathbf{y}>=\mathbf{x}^T\mathbf{y}=0$ the vectors are orthogonal and anything else they aren't

4. Hey guys thanks for replying. Im still a little confused though. Tonio, did you mean that they ARE perpendicular? If so, I understand what to do.

5. Originally Posted by crakapete
Hey guys thanks for replying. Im still a little confused though. Tonio, did you mean that they ARE perpendicular? If so, I understand what to do.

In fact I meant that u and v aren't perpendicular...and yes : u and w are.

Tonio