v = <3,0,0> and w = <0,1,-1> Determine u = v x w using the geometric properties of the cross product rather than the formula.

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- Apr 13th 2009, 07:06 PMLink88Cross Product
v = <3,0,0> and w = <0,1,-1> Determine u = v x w using the geometric properties of the cross product rather than the formula.

- Apr 13th 2009, 07:37 PMProve It
I'm a little rusty at this, so if anyone wants to correct my logic, please do so.

The cross-product gives a vector (in this case u), which is orthogonal to both v and w.

i.e. u is normal to the plane that v and w lie on, and also has the same coefficients as that plane.

So find the plane that v and w lie on, and then you have the normal, and so you have the cross product.