Vector Basics: Finding V1 and V2 | Homework Statement and Equations

[jrm2002]

Homework Statement

I have two vectors V1 and V2.
V1 is parallel to xz plane
V2 is perpendicular to V1
V2 is 10 units.Can i get V1?

Homework Equations

The Attempt at a Solution

Force triangle?Can''t solve?

 

[genneth]

You can only get V1's direction, not magnitude.

 

[jrm2002]

How can we get the direction of V1?

 

[Dick]

The normal to the xz plane is the vector V3=(0,1,0). If V1 is parallel to the xz plane then it is perpendicular to V3. So V1 is perpendicular to V2 and V3. So a direction for V1 is given by the vector cross product of V2xV3.

 

[uiulic]

But from the given conditions, v2 (only the magnitude is known) is not given, how can you know v1's direction ?

 

[Dick]

The direction is the same as v2x(0,1,0). That's about all you can say. And if v2 is parallel to (0,1,0) then you can't say much of anything at all.

 

[jrm2002]

You said:
what will be the value of cross product V2 x V3?

 

[jrm2002]

My question:

what will be the value of cross product V2 x V3?

 

[Dick]

My question:

what will be the value of cross product V2 x V3?

Ok, shorter answer. NO. You can't 'get' V1.

 

[jrm2002]

But what will be the cross product V2 x V3, in an expression?

 

[Dick]

If V2=(x,y,z), (x,y,z)x(0,1,0)=(-z,0,x) (look up cross product). The result is in the xz plane is perpendicular to V2.

 

[jrm2002]

Plz help with another case:

1. If V2 and V3 are parallel
2. Hence V1 = the cross product of V2 x V3 evaluates to 0,0,0
3. What is the physical reason for this?

 

[Dick]

The cross product is related to the area of the parallelogram created by the two vectors. What happens if they are parallel?

 

[jrm2002]

Straight line?

 

[Dick]

If you mean what I think you mean then yes. The area is zero. So the vector is zero.