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Darina [25.2K]
3 years ago
8

Find the unit vector in the direction of v=(7,-3). (enter exact answers with square roots)

Mathematics
1 answer:
navik [9.2K]3 years ago
8 0

Answer:

\binom{ \frac{7 \sqrt{58} }{58} }{  \frac{ - 3 \sqrt{58} }{58} }

Step-by-step explanation:

First, find the magnitude of the vector:

|v|  =  \sqrt{( {(7)}^{2} + {( - 3)}^{2})  } \\  =  \sqrt{(49 + 9)}  \\   =  \sqrt{58}

Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:

unit \: vector =  \binom{ \frac{7}{ \sqrt{58} } }{ \frac{ - 3}{ \sqrt{58} } }  \\  =  \binom{ \frac{7 \sqrt{58} }{58} }{  \frac{ - 3 \sqrt{58} }{58} }

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