The correct option is A ^k, 20 m/s
It is given that
→ω=(2^i+^j) and →r=(−4^i+8^j)
So, →v=→ω×→r
i.e →v=∣∣
∣
∣∣^i^j^k210−480∣∣
∣
∣∣
=(0−0)^i−(0−0)^j+(16+4)^k=20^k
Hence, linear velocity →v=20^k m/s
Alternate solution:
We know that →v=→ω×→r
Applying Right hand rule, the direction of →v is along ^k direction.
Checking the angle between the vectors,
→ω.→r=(2^i+^j).(−4^i+8^j)=8−8=0
∴ →ω⊥→r
Hence, →v=→ω×→r=rωsin 90∘
i.e v=(√(−4)2+(8)2)(√(2)2+(1)2)sin90∘
=√400=20 m/s