Answer

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**Hint:**We will try to understand the question first then arrange each data one by one and finally by applying \[6m/s\] and many other formulas along with this we will get the accurate answer.

**Complete answer:**

The velocity of boat with respect to river or Vbr\[ = 4 \uparrow .\] Let us assume that East is our X axis is North is our Y axis. Velocity or river or \[{V_r} = 2 \uparrow \]

Here,

\[

{V_b} = 2 \uparrow + 4J \\

\overrightarrow {{V_b}_r} = {\overrightarrow V _b} - \overrightarrow {{V_r}} \\

\overrightarrow {{V_b}} = \overrightarrow {{V_{br}}} + \overrightarrow {{V_r}} \\

\]

Velocity of wind \[\left( {{V_w}} \right) = 6J\]

Velocity of wind with respect to the boat is referred as \[\left( {{V_{wb}}} \right)\]

\[

\therefore \overrightarrow {{V_{wb}}} = \overrightarrow {{V_w}} - \overrightarrow {{V_b}} \\

= 6J - \left( {2 \uparrow + 4J} \right) \\

= - 2 \uparrow + 2J \\

\]

\[\therefore \]Direction of the flag is in the North West.

**Hence, the correct answer is North West direction.**

**Note:**Boat velocity is \[4m/s\] towards east is \[4J\]. Velocity of wind is \[6m/s\]. To solve the other boat problems, we need to understand other many formulas for eg: The speed of a boat relative to the water is equal to the speed of the boat in still water.

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