Final answer:
To find a unit vector that is orthogonal to both vector A and vector B, we can use the cross product. The cross product of two vectors produces a vector that is perpendicular to both of them.
Step-by-step explanation:
To find a unit vector that is orthogonal to both vector A and vector B, we can use the cross product. The cross product of two vectors produces a vector that is perpendicular to both of them. The magnitude of the cross product is given by the product of the magnitudes of the two vectors and the sine of the angle between them. The direction of the cross product can be determined using the right-hand rule.
Let's assume that vector A = Axi + Ayj + Azk and vector B = Bxi + Byj + Bzk.
The cross product of vector A and vector B is given by:
A x B = (AyBz - AzBy)i + (AzBx - AxBz)j + (AxBy - AyBx)k
This cross product vector will be orthogonal to both vector A and vector B. To obtain the unit vector, we can divide the cross product vector by its magnitude.