Final answer:
To find a unit vector perpendicular to vector v, we can use the vector product or cross product. The formula p = (v x k)/|v x k| can be used, where k is a vector pointing in the z-direction and |v x k| represents the magnitude of the cross product.
Step-by-step explanation:
In order to find a unit vector perpendicular to vector v, we can use the vector product or cross product. The vector product of two vectors A and B is a vector perpendicular to both A and B with a magnitude equal to the product of their magnitudes multiplied by the sine of the angle between them.
To find vector p, we can use the formula p = (v x k)/|v x k|, where k is a vector pointing in the z-direction (perpendicular to the x-y plane) and |v x k| represents the magnitude of the cross product.
For example, if vector v is given by v = (2i - 3j + 4k), we can find vector p as p = (v x k)/|v x k|, where k = (0i + 0j + 1k). By calculating the cross product, we obtain p = (-3i -2j + 0k)/√(9 + 4) = (-3i - 2j)/(√13).