Final answer:
The unit vector orthogonal to both î x ĵ (i j) and î x (i k) is the unit vector î itself.
Step-by-step explanation:
To find a unit vector that is orthogonal to both i j and i k, we can use the cross product of the two vectors. Remember, the cross product of two vectors results in a third vector that is orthogonal to both. Using the provided Equation 2.38, we find that cross products of the standard unit vectors (i.e., î, ĵ, and k) that appear in cyclic order yield a unit vector that is orthogonal to the two. In the case of î x ĵ, the result is +k. Similarly, crossing ĵ and k gives î, and crossing k and î gives ĵ.
However, the question asks for the vector orthogonal to î x ĵ (i j) and î x k (i k). Using the rules stated for cross products, we can deduce that since î x ĵ = k and î x k = -ĵ (following the anti-cyclic rule), the only vector orthogonal to both k and -ĵ is î. Therefore, î itself is the unit vector orthogonal to both î x ĵ and î x k.