Given that p = 2i – 5j and q = i – 3j, find the unit vector in the direction of 3p – 4q.

1. (a)Given that p = 2i – 5j and q = i – 3j, find the unit vector in the direction of 3p – 4q.[4]
2. (b)A river flows between parallel banks at a speed of 1.25kmh⁻¹. A boy standing at point A on one bank sends a toy boat across the river to his father standing directly opposite at point B. The toy boat, which can travel at vkmh⁻¹ in still water, crosses the river with resultant speed 2.73 kmh⁻¹ along the line AB. [Figure 8.1]
3. (b)(i)Calculate the value of v.[2]
4. (b)(ii)The direction in which the boy points the boat makes an angle θ with the line AB. Find the value of θ.[2]

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