The magnitude of a resultant vector is:

$\overline{){\mathbf{\left|}}{\mathbf{R}}{\mathbf{\right|}}{\mathbf{=}}\sqrt{\mathbf{|}\mathbf{A}{\mathbf{|}}^{\mathbf{2}}\mathbf{+}\mathbf{|}\mathbf{B}{\mathbf{|}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{\left|}\mathbf{A}\mathbf{\right|}\mathbf{\left|}\mathbf{B}\mathbf{\right|}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta}}}$, where θ is the angle between the two vectors A and B.

We're told that the golfer is taking three strokes, A, B, and C to sink the ball.

These points in their components can be taken to be:

(A_{x}, A_{y}), (B_{x}, B_{y}), and (C_{x}, C_{y}).

Vector C is making an angle of 30.0° west of south.

The resultant of these three vectors will have components (A_{x} + B_{x} + C_{x}, A_{y }+B_{y} + C_{y})

The components of A:

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast (45°), and 1.00 m at 30.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

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