Find the angle between the given vectors to the nearest tenth of a degree. u = <8, 7>, v = <9, 7>

Asked by maham237 @ in Mathematics viewed by 315 People

u = <8, 7>, v = <9, 7>

Answered by maham237 @


Angle θ between two vectors is given by, \theta =cos^{-1}( \frac{u&#10; \cdot v}{|u||v|} ); where u \cdot &#10;v=8(9)+(7)(7)=72+49=121; |u|= \sqrt{ 8^{2} + 7^{2} } = &#10;\sqrt{64+49} = \sqrt{113} and |v|=\sqrt{ 9^{2} + 7^{2} } = &#10;\sqrt{81+49} = \sqrt{130}.
Therefore, \theta =cos^{-1}( \frac{121}{ \sqrt{113} \times \sqrt{130} } )=cos^{-1}0.9983=3.3^o

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