Question 165567
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+4j}}}
{{{M[r]=sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5}}}
{{{r[u]=(3/5)i+(4/5)j}}}
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ii) {{{r=12i-5j}}}
{{{M[r]=sqrt(12^2+5^2)=sqrt(144+25)=sqrt(169)=13}}}
{{{r[u]=(12/13)i+(-5/13)j}}}.
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iii) {{{r=-2i-2j-5k}}}
{{{M[r]=sqrt(2^2+2^2+5^2)=sqrt(4+4+25)=sqrt(33)}}}
{{{r[u]=(-2/sqrt(33))i+(-2/sqrt(33))j+(5/sqrt(33))k}}}
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iv) {{{r=i+2j+3k}}}
{{{M[r]=sqrt(1^2+2^2+3^2)=sqrt(1+4+9)=sqrt(14)}}}
{{{r[u]=(1/sqrt(14))i+(2/sqrt(14))j+(3/sqrt(14))k}}}