Vectors and scalar projections

[hnnhcmmngs]

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?

 

[berkeman]

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?

 

[LCKurtz]

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:$$
\vec A \cdot \vec B \times \vec C = \vec A \times \vec B \cdot \vec C$$