Unit Vector (u)

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 Specifies the direction of a vector (like standing at the tail and point to the tip)
 Points in the direction of the vector & “gives direction” (to make it a vector)
 “unit-less”
 magnitude of 1
the unit vector =  (any vector / magnitude of that vector)



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In the figure below, you can see the unit vector U pointing to the tip of vector V

EX:  Given vector A as (4i+2J+4k)m. Build the unit vector for A.                                                   

vectorA = A uA

the magnitude of A = Ax2 + Ay2 + Az2\sqrt{Ax^{2}\ +\ Ay^{2}\ +\ Az^{2}}Ax2 + Ay2 + Az2​ = 6

therefore, uA = vectorA / magA = 0.67i+0.33j+0.67k

 (0.67i+0.33j+0.66k)

Find a vector whose length is one, that points in the same direction as the vector u⃗=<2, 1, −2>\vu = \rowvecth{2}{1}{-2}u=⟨2,1,−2⟩

<−23, −13, 23>\rowvecth{-\tfrac23}{-\tfrac13}{\tfrac23} ⟨−32​,−31​,32​⟩

<29, 19, −29>\rowvecth{\tfrac29}{\tfrac19}{-\tfrac29} ⟨92​,91​,−92​⟩

<−29, −19, 29>\rowvecth{-\tfrac29}{-\tfrac19}{\tfrac29} ⟨−92​,−91​,92​⟩

<23, 13, −23>\rowvecth{\tfrac23}{\tfrac13}{-\tfrac23} ⟨32​,31​,−32​⟩

I don't know

Practice Question: Unit Vector
Which one of the following is not a unit vector?

a.) (0,−1)(0,-1)(0,−1)

b.) (12,12)\left(\sqrt{\frac{1}{2}},\sqrt{\frac{1}{2}}\right)(21​​,21​​)

c.) (12,−12)\left(\sqrt{\frac{1}{2}},-\sqrt{\frac{1}{2}}\right)(21​​,−21​​)

d.) (14,34)\left(\frac{1}{4}, \frac{3}{4}\right)(41​,43​)

e.) (−35,−45)\left(-\frac{3}{5}, -\frac{4}{5}\right)(−53​,−54​)

I don't know

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EX:  Given vector B as (3i-2J+8k)m. Build the unit vector for B.

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Wize University Physics Textbook (Master) > Force Vectors (Advanced Info)

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Practice Question: Unit Vector