Solve (d1 + d2) . (d1 x 4d2): Unit Vector Question

[Shatzkinator]

Homework Statement

If d1 = 3i - 2j +4k and d2 = -5i + 2j -k, then what is (d1 + d2) . (d1 x 4d2)?

Homework Equations

c = absin(theta) --> vector product
c = abcos(theta) --> scalar product

The Attempt at a Solution

I looked at a sample problem and they show the distributive law for components, however one of the calculations was 3i x 3k = 9(-j)... how does that work (ie. using the above formula does not take into account any of the letters or unit vectors or whatever)? Second, how do you know if its vector or scalar product. Thanks a bunch...

 

[LowlyPion]

Homework Statement

If d1 = 3i - 2j +4k and d2 = -5i + 2j -k, then what is (d1 + d2) . (d1 x 4d2)?

Homework Equations

c = absin(theta) --> vector product
c = abcos(theta) --> scalar product

The Attempt at a Solution

I looked at a sample problem and they show the distributive law for components, however one of the calculations was 3i x 3k = 9(-j)... how does that work (ie. using the above formula does not take into account any of the letters or unit vectors or whatever)? Second, how do you know if its vector or scalar product. Thanks a bunch...

Welcome to PF.

What you basically have is the scalar triple product.

(d1 + d2) dot (d1 x 4d2)

To resolve it you need to first add the (d1 + d2) term.
Then perform the Cross Product of (d1 x 4d2).
Then the Dot product of the results of the first 2 steps.

http://en.wikipedia.org/wiki/Scalar_triple_product#Scalar_triple_product