Question

Find the vector, not with determinants, but by using properties of cross products. k × (i − 7j)

Answer 1

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.

1. First, find the cross product of i × j which is equal to k (positive z-axis).
2. Then, find the cross product of −7j × k which is equal to 7i (positive x-axis).
3. Add the two cross products together: 7i + k.

Therefore, the vector k × (i − 7j) is equal to 7i + k.