'09 TMSCA #10

[nsguy1350]

48. Let u = <2,4,6> and v = <-3,-5,-7>. If u x v = <a,b,c>, find a + b + c.

Did 55 (correctly), missed 2, skipped 3, for a total of 326, the lowest of 3 tests today! Today, I got 330, 331, 326, which are scores I had never reached before, and I got them all today! Improving slowly... need to dominate TMSCA State!

[michel470]

Let u = <2,4,6> and v = <-3,-5,-7>. If u x v = <a,b,c>, find a + b + c.

The way I was taught to do this in pre-cal/college algebra(can't remember which) was to put the values in a three by three matrix
i j k
2 4 6
-3 -5 -7
The i, j, and k are always in the first row, they are called unit vectors and correspond to the x,y, and z values of the vectors given( <x,y,z>, <i,j,k>) Notice all the x values(2 and -3 are under the i, the y-values under the j, the z values under the k).

To find a, cross out the row and column that i is in, and you are left with a 2X2 matrix:
4 6
-5 -7
Take the determinant of this matrix(-28 - (-30)= 2), so your value for a is 2

To find b, cross out the row and column that j is in, and the resulting numbers are your 2X2 matrix
2 6
-3 -7
Take the determinant of this matrix(-14 - (-18)=4) so your value for b is 4

To find c, cross out the row and column that k is in, and you're left with ANOTHER 2X2 matrix(it's pretty methodical)
2 4
-3 -5
take the determinant(-10 - (-12)=2) so your value for c is 2

SO.... a + b + c = 2 + 4 + 2= 8

This shouldn't take too long once you have it down...
Hope that helps you out some, let me know if I can make anything clearer and best of luck on your goals

[nsguy1350]

Thanks! This is the cross product, correct?

[michel470]

I believe so.