How do you find the unit vector having the same direction as vector u = i - 6 j + 5 k?

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Answer 1 · 2016-07-01T10:48:17

Thus $" "hat(u)=1/sqrt(61)i-6/sqrt(61)j+5/sqrt(61)k$

Or if you prefer

$" "hat(u)=sqrt(61)/61i-(6sqrt(61))/61j+(5sqrt(61))/61k$

Given that $vec(u)=i-6j+5k$

Then $||u||=sqrt(1^2+(-6)^2+5^2)" "=" "sqrt(61)$

Not that 61 is a prime number

Thus $" "hat(u)=1/sqrt(61)i-6/sqrt(61)j+5/sqrt(61)k$

Or if you prefer

$" "hat(u)=sqrt(61)/61i-(6sqrt(61))/61j+(5sqrt(61))/61k$