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[/I]The second question talks about finding the right direction to move in.

2) A man wished to row across a lake to a point directly south of him. If the lake has a current flowing west at 3km/hr and he can row at 7km/hr, find the direction in which he must row.

Draw a rough sketch: You'll get a right triangle with one leg pointing South and one leg pointing $\displaystyle East$ because the man has to componsate the current running West. The course is described by the hypotenuse. Use the Sine function to calculate the angle of deviation from South.
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The fourth question was about vector products, which I'm pretty sure I have a good grasp on. Still, an elaboration on how to work them out would be nice, just so I can be sure I've done it right.

4) Find the vector product:

*(2i - j)* x

*(6i + 3j + 2k)*

I've got:

[I]let a = 2i = j, b = 6i + 3j + 2k

a * b =

| i j k |

| 2

**-**1 0|

<<<<<< there is a negative sign missing
|6 3 2|

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=

i( (

**-**1)(2) - (0)(3) ) - j( (2)(2) - (0)(6) ) + k( (2)(3) - (

**-**1)(6) )

**= -2i - 4j + 12k**
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