Final answer:
To find the vector k × (i − 7j) without using determinants but by using properties of cross products, we can use the fact that the cross product is anticommutative.
Step-by-step explanation:
To find the vector k × (i − 7j) without using determinants but by using properties of cross products, we can use the fact that the cross product is anticommutative. The result of the cross product is a vector that is perpendicular to both vectors being crossed.
- First, find the cross product of i × j which is equal to k (positive z-axis).
- Then, find the cross product of −7j × k which is equal to 7i (positive x-axis).
- Add the two cross products together: 7i + k.
Therefore, the vector k × (i − 7j) is equal to 7i + k.