Dot product and cross product problem

[tballs]

I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX.

For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)

A = 4I -3J -2K B = -3I +1J +2K C = -3I + 5J -4K

Homework Equations

I J K I J
4 -3 -2 4 -3
-9 3 6 -9 3

(18I+6I) + (18J-24J) + (-27K-12K)
24I - 6J - 39K

(24I X -3I) + (-6J X 5J) + (-39K X -4K)

-72I -30J +156

156-102

54

 

[and9]

I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX.

For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)

A = 4I -3J -2K B = -3I +1J +2K C = -3I + 5J -4K

Homework Equations

I J K I J
4 -3 -2 4 -3
-9 3 6 -9 3

(18I+6I) + (18J-24J) + (-27K-12K)
24I - 6J - 39K

(24I X -3I) + (-6J X 5J) + (-39K X -4K)

-72I -30J +156

156-102

54

Do the cross product first, the three in front of B is a constant and can be pulled out of the cross product (or you can multiply three into all of the components of B, either works).

Cross product by components:
(A(J)*(B(K) - B(J)*A(K))I - (A(I)*B(K) - B(I)*A(K))J + (A(I)*B(J) - B(I)*A(J))K

Then dot product is just multiplying each component and summing them.

(A(I)*B(I)) + (A(J)*B(J)) + (A(K)*B(K)) and that should give you a number (or a scalar).

I hope the notation makes sense. A/B then the I, J, or K component of that vector is inside of parentheses.

Have fun with multivariate calc/linear algebra junk

 

[tballs]

thank you I figured it out.