Vectors and scalar projections

  • #1
hnnhcmmngs
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Homework Statement



Let a and b be non-zero vectors in space. Determine comp a (a × b).

Homework Equations



comp a (b) = (a ⋅ b)/|a|

The Attempt at a Solution


[/B]
comp a (a × b) = a ⋅ (a × b)/|a| = (a × a) ⋅b/|a| = 0 ⋅ b/|a| = 0
Is this the answer? Or is there more to it?
 
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  • #2
I don't know if your work is mathematically correct, but what can you say about the direction of the resultant of a x b compared to the direction of a? And what is the dot product of two vectors that have that directional relationship? :smile:
 
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  • #3
hnnhcmmngs said:

Homework Statement



Let a and b be non-zero vectors in space. Determine comp a (a × b).

Homework Equations



comp a (b) = (a ⋅ b)/|a|

The Attempt at a Solution


[/B]
comp a (a × b) = a ⋅ (a × b)/|a| = (a × a) ⋅b/|a| = 0 ⋅ b/|a| = 0
Is this the answer? Or is there more to it?
Your work is correct assuming that you have proven the formula that you can interchange dot and cross in a triple scalar product:$$
\vec A \cdot \vec B \times \vec C = \vec A \times \vec B \cdot \vec C$$
 
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