Final answer:
The cross product k x (i - 3j) can be found by separately calculating the cross products of unit vectors based on their cyclic order, resulting in the final vector 3i - j.
Step-by-step explanation:
The question asks us to find the vector resulting from the cross product k x (i - 3j) without using determinants, but rather by utilizing the properties of cross products. Using the properties of cross products for unit vectors, we know that the cross product of two different unit vectors is always another unit vector, and its direction depends on the cyclic order of i, j, and k.
For the given cross product, we calculate each component separately:
- k x i (considering the cyclic order, k follows j and comes before i) gives us -j.
- For k x -3j (as k follows i and comes before j), the result is 3i.
Therefore, combining these results, the final vector is 3i - j.