Vector product

Let u and v linearly independent vectors. How do we determine all the vectors that are orthogonal to both of them?

We can suppose that:

We name this vector
cross or vector product of u and v .

- Its magnitude is:
- Its direction is perpendicular to u and v.
- Its sense is determined by the “corkscrew rule”  or “right-hand rule”                        
(vii) The area of the parallelogram formed by u and v is the magnitude of its vector product.




Exercise: Let A(1,1,1),B(2,-1,0),C(3,3,-2). Calculate:

a) ABxAC

b) A unit vector orthogonal to AB and AC

c) The area of the parallelogram defined by the vectors AB and AC

d) The area of the triangle ABC




Solutions: a) (-4,1,-2); b) (-4√21/21,√21/21,-2√21/21); c) √21u2; d) √21/2u2

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