review the graph. which statement accurately describes the vector shown? magnitude of \\( \\sqrt { 11 } \\)…

Answer:

magnitude of (\sqrt{61}) and direction angle equal to approximately (50^{\circ})

Explanation:

Step1: Calculate the magnitude

If the vector has components ((x = 6,y = 5)) (assuming from the graph, as starting from origin ((0,0)) to ((6,5))), the magnitude (r) of a vector (\vec{v}=(x,y)) is given by the formula (r=\sqrt{x^{2}+y^{2}}). Substitute (x = 6) and (y = 5) into the formula: (r=\sqrt{6^{2}+5^{2}}=\sqrt{36 + 25}=\sqrt{61}).

Step2: Calculate the direction angle

The direction angle (\theta) of a vector (\vec{v}=(x,y)) is given by (\tan\theta=\frac{y}{x}). Here, (x = 6) and (y = 5), so (\tan\theta=\frac{5}{6}). Using a calculator, (\theta=\arctan(\frac{5}{6})\approx39.8^{\circ}\approx40^{\circ}) (if we consider the wrong - component assumption) or if we assume the vector from ((0,0)) to ((5,6)) (maybe mis - reading the graph coordinates in a wrong initial analysis, but if we recalculate with (x = 5) and (y = 6)): Magnitude (r=\sqrt{5^{2}+6^{2}}=\sqrt{25 + 36}=\sqrt{61}), and (\tan\theta=\frac{6}{5}), (\theta=\arctan(\frac{6}{5})\approx50.2^{\circ}\approx50^{\circ})