A sailor in a boat, which is going due east with a speed of `8m//s` observes that a submarine is heading towards north at a speed of `12m//s` and sinking at a rate of `2 m//s`.The commander of submarine observes a helicopter ascending at a rate of `5 m//s` and heading towards west with `4 m//s`.Find the speed of the helicopter with respect to boat.

Explanation

To find the speed of the helicopter with respect to the boat, we will break down the problem into manageable steps.

### Step 1: Define the Directions
We will define our coordinate system:
- East direction as \( \hat{i} \)
- North direction as \( \hat{j} \)
- Upward direction as \( \hat{k} \)

...