SOLUTION: find a unit vector along each of the following vectors; (i) r=3i^+4j^ (ii)r=12i^-5j^ (iii)r=-2i^-2j^-5k^ (iv)r=i^+2j^+3k^

Algebra ->  Vectors -> SOLUTION: find a unit vector along each of the following vectors; (i) r=3i^+4j^ (ii)r=12i^-5j^ (iii)r=-2i^-2j^-5k^ (iv)r=i^+2j^+3k^      Log On


   



Question 165567: find a unit vector along each of the following vectors;
(i) r=3i^+4j^ (ii)r=12i^-5j^ (iii)r=-2i^-2j^-5k^ (iv)r=i^+2j^+3k^

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the unit vector in the direction of the given vector, divide the vector by its magnitude,M.
This way it has the same direction and magnitude of 1.
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i) r=3i%2B4j
M%5Br%5D=sqrt%283%5E2%2B4%5E2%29=sqrt%289%2B16%29=sqrt%2825%29=5
r%5Bu%5D=%283%2F5%29i%2B%284%2F5%29j
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ii) r=12i-5j
M%5Br%5D=sqrt%2812%5E2%2B5%5E2%29=sqrt%28144%2B25%29=sqrt%28169%29=13
r%5Bu%5D=%2812%2F13%29i%2B%28-5%2F13%29j.
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iii) r=-2i-2j-5k
M%5Br%5D=sqrt%282%5E2%2B2%5E2%2B5%5E2%29=sqrt%284%2B4%2B25%29=sqrt%2833%29
r%5Bu%5D=%28-2%2Fsqrt%2833%29%29i%2B%28-2%2Fsqrt%2833%29%29j%2B%285%2Fsqrt%2833%29%29k
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iv) r=i%2B2j%2B3k
M%5Br%5D=sqrt%281%5E2%2B2%5E2%2B3%5E2%29=sqrt%281%2B4%2B9%29=sqrt%2814%29
r%5Bu%5D=%281%2Fsqrt%2814%29%29i%2B%282%2Fsqrt%2814%29%29j%2B%283%2Fsqrt%2814%29%29k