Unit vector perpendicular to the vectors i, k is

here are the solutions for questions 35, 36, 42, 43, and 44.

Question 35:
Unit vector perpendicular to the vectors $\hat{i}$, $\hat{k}$ is

To find a vector perpendicular to two given vectors, we compute their cross product.
Let $\vec{u} = \hat{i}$ and $\vec{v} = \hat{k}$.

Step 1: Calculate the cross product $\vec{u} \times \vec{v}$.

$$\vec{u} \times \vec{v} = \hat{i} \times \hat{k}$$

Using the right-hand rule or the determinant formula: