Given, ω⃗=2^k and r⃗=2^i+2^j. Find the linear velocity.

Linear velocity of an object, v⃗=ω⃗ × r⃗ where, ω⃗ is the angular velocity of object about a point r⃗ is the position vector of object from the point. Thus, v⃗=(2^k) × (2^i+2^j)=-4^i+4^j