Final answer:
The cross product of the vectors (i→ j→)×(i→−j→) is calculated using the properties of cross products and is found to be -k.
Step-by-step explanation:
We are asked to find the cross product (i→ j→)×(i→−j→).
Using the properties of cross products and the geometric definition, we know that:
- i×i = j×j = k×k = 0, because the cross product of any vector with itself is zero.
- For any pair of different unit vectors, the result is the third unit vector, following a cyclic order.
- If the two unit vectors are reversed in order, the resulting unit vector is negative.
Now, applying these rules:
- i×i = 0 and j×j = 0, since they are the same unit vectors.
- Then we have i×(-j) = -(i×j).
- From the cyclic order (i, j, k), we have i×j = k, so i×(-j) = -k.
- Therefore, the result is 0i + 0j + (-k), which simplifies to -k.
The cross product of the vectors (i→ j→)×(i→−j→) is -k.