dot product and cross product

[soccerball3211]

For the following three vectors, what is 7.00 C · (-6.00 A×B)?

vector A= 2(i hat) + 3(j hat) - 4(k hat)
vector B= -3(i hat) + 4(j hat) + 2(k hat)
vector C= 7(i hat) - 8(j hat)

For an answer I got -6468?

Is this a reasonable answer or am I way off?

 

[soroban]

Hello, soccerball3211!

I got a different answer . . . but I could be wrong.

Given: \(\displaystyle \,\begin{array}{ccc}\vec{A}\:=\:\langle 2,\,3,\,-4\rangle \\ \vec{B} \:=\:\langle -3,\,4,\,2\rangle \\ \vec{C}\:=\:\langle 7,-8,\,0\rangle\end{array}\)

Find: \(\displaystyle \,-7C\,\cdot\,(-6A\,\times\,B)\)

First of all: \(\displaystyle \,7C\,\cdot\,(-6A\,\times\,B) \;= \;-42C\,\cdot\,(A\,\times\,B)\)


\(\displaystyle A\,\times\,B\;=\;\begin{vmatrix} i & j & k \\ 2 & 3 & -4 \\ -3 & 4 & 2\end{vamtrix} \;= \;i(6\,+\,16)\,-\,j(4\,-\,12)\,+\,k(8\,+\,9) \;=\;\langle 22,\,8,\,17\rangle\)

Then:\(\displaystyle \:C\,\cdot\,(A\,\times\,B) \;=\;\langle7,-8,\,0\rangle\,\cdot\,\langle22,\,8,\,17\rangle \;= \;(7)(22)\,+\,(-8)(8)\,+\,(0)(17) \;=\;90\)

Finally: \(\displaystyle \,-42C\,\cdot\,(A\,\times\,B)\;=\;-42(90)\;=\:-3780\)

 

[pka]

I also get -3780.