Sector =icap-kcapB vector =jcap-icapCross product of it

We are given two vectors:

Sector = î - k̂
Vector B = ĵ - î

We need to find their cross product:

A × B = (î - k̂) × (ĵ - î)

Step 1: Expand the Cross Product
Using the distributive property of cross products:

A × B = î × ĵ - î × î - k̂ × ĵ + k̂ × î

We now evaluate each term:

î × ĵ = k̂
î × î = 0 (since the cross product of any vector with itself is zero)
k̂ × ĵ = -î (using the right-hand rule)
k̂ × î = ĵ
Step 2: Substitute the Values
A × B = k̂ - 0 - (-î) + ĵ

A × B = k̂ + î + ĵ

Final Answer:
A × B = î + ĵ + k̂