If the position vector of a particle is ⃗r=(3ˆi+4ˆj) met

Question

If the position vector of a particle is

⃗ r = (3 ˆ i + 4 ˆ j)

meter and its angular velocity is

⃗ ω = (ˆ j + 2 ˆ k)

rad/sec then its linear velocity is (in m/s)

Options:

A . (8ˆi−6ˆj+3ˆk)

B . (3ˆi+6ˆj+8ˆk)

C . -(3ˆi+6ˆj+6ˆk)

D . (6ˆi+8ˆj+3ˆk)

Answer: Option A
:
A

⃗ v = ⃗ ω \times ⃗ r = (3 ˆ i + 4 ˆ j + 0 ˆ k) \times (0 ˆ i + ˆ j + 2 ˆ k) = ∣ ∣∣∣ ∣ \begin{matrix} ˆ i & ˆ j & ˆ k 3 & 4 & 0 0 & 1 & 2 \end{matrix} ∣ ∣∣∣ ∣ = 8 ˆ i - 6 ˆ j + 3 ˆ k

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