Final answer:
The unit vector that is orthogonal to both i j and i k is i, which is the unit vector along the x-axis.
Step-by-step explanation:
To find a unit vector that is orthogonal to both i j and i k, we need to recognize that i, j, and k are the unit vectors along the x, y, and z axes respectively. Since the cross product of two vectors results in a vector orthogonal to both, we can use the cross product of i and j to indirectly find our solution. Given the knowledge that the cross product of two different unit vectors results in the remaining unit vector, we can assert that i x j = k, and i x k = -j. Therefore, since we want a vector orthogonal to both i j and i k, which correspond to k and -j, respectively, the unit vector that is orthogonal to both k and -j is simply i, the unit vector along the x-axis.