Final answer:
The cross product (AxB) of vectors A=(-5i + 6j - 3k) and B=(3i + 4j + 2k) is calculated using the components of A and B and results in (AxB) = (24i + 1j - 38k).
Step-by-step explanation:
To determine the cross product (AxB) of two vectors A=(-5i + 6j - 3k) and B=(3i + 4j + 2k), you can use the definition of the cross product for vectors in three-dimensional space. The cross product of two vectors results in a third vector that is perpendicular to the plane containing the first two vectors. The calculation involves the determinants of a matrix formed by the unit vectors i, j, and k, and the components of vectors A and B.
The cross product is calculated as follows:
- AxB = [(AyBz - AzBy)i
- + (AzBx - AxBz)j
- + (AxBy - AyBx)k]
For our specific vectors A and B, substituting the given components:
- AxB = [((6)(2) - (-3)(4))i
- + ((-3)(3) - (-5)(2))j
- + ((-5)(4) - (6)(3))k]
Therefore, after performing the multiplications and additions:
- AxB = [(12 + 12)i
- + (-9 + 10)j
- + (-20 - 18)k]
Which simplifies to: