please help?

Question

What is the easiest way to solve this vector product:
(5i-j+3k) x (i+3j+2k).(without matrix or determinant)
Do u know any easiest way or tricks to solve this problem?
please tell me. this is a cross product problem.

Answer 1

Check your earlier posts!

The easiest way is with technology: graphing calculators or computer algebra systems. With Maple I find:

> with(linalg):
Warning, new definition for norm
Warning, new definition for trace
> crossprod([5,-1,3],[1,3,2]);
[-11, -7, 16]

"By hand" methods are (1) memorize the key formula

[a,b,c]x[x,y,z]=[b*z-c*y, c*x-a*z, a*y-b*x]

or (2) if you know determinants, you find the determinant of the matrix with i,j,k in the first row, one vector in the 2nd row and the other vector in the third row.