hence angle between vectors is option a ,173 degree
When an equation has both direction as well as magnitude it refers to vector equation.
Formula used [tex]\alpha =cos^{-1} (\frac{u.v}{|u||v|})[/tex]
u.v=1*(-1)+[tex]\sqrt{7} *(-4)[/tex]
|u|=[tex]\sqrt{ 1^{2} +\sqrt{7} ^{2}}[/tex]=[tex]2\sqrt{2}[/tex]
|v|=[tex]\sqrt{ (-1^{2}) +(-4^{2})[/tex]=[tex]\sqrt{17}[/tex]
[tex]\alpha =cos^{-1} (\frac{-1-4\sqrt{7} }{|2\sqrt{2} ||\sqrt{17} |})[/tex]
[tex]\alpha =cos^{-1} (\frac{-1-10.58}{2.82*4.12})[/tex]
[tex]\alpha =cos^{-1} (\frac{-11.58}{11.61})[/tex]
[tex]\alpha =cos^{-1} (-0.99)[/tex]
hence option a 173 degree is correct
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