For what value(s) of c will 1/5i-1/5j+ck be a unit vector?

For the solution to this equation. We write:
1/25+1/25+c^2=1

However, I fail to understand why we can equate the vector to 1 as other unit vectors don't add up to 1 either.

Question

For what value(s) of c will 1/5i-1/5j+ck be a unit vector?

For the solution to this equation. We write:
1/25+1/25+c^2=1

However, I fail to understand why we can equate the vector to 1 as other unit vectors don't add up to 1 either.

anonymous · Answer

(will be back in 20)

anonymous · Answer

solution is given here 1A-2: http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-a-vectors-determinants-and-planes/problem-set-1/MIT18_02SC_SupProbSol1.pdf

anonymous · Answer

whats your doubt ? 
magnitude of unit vector = 1