Mathematics

Problem

(a) Derive a general expression for the unit vector along any two–dimensional vector

\mathbf{V}=V_{x}\,\hat i + V_{y}\,\hat j

. a. (i) Show the steps leading to the expression for the unit vector in terms of

V_{x}

and

V_{y}

. b. (ii) An aircraft’s velocity is

\mathbf{v}=2.5\times10^{2}\,\hat i - 4.0\times10^{2}\,\hat j\,\text{m s}^{-1}

. Calculate the magnitude of this velocity and the direction it makes with the positive x–axis, taking clockwise angles as positive. c. (iii) Using your result from part (i), write the unit vector in the direction of the aircraft’s velocity, giving components to three significant figures.

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