Magnitude of a projection

Question

I don't know where I am going wrong, but I am trying to calculate the magnitude of the vector $-\tfrac4{13}(3, -1, 4)$.

So I used the formula $||v|| = \sqrt{x^2 + y^2 + z^2}$ but I kept getting an undefined value. I multiplied each of 3, -1 and 4 by -4/13 and used them as my x, y and z values respectively.

My calculation:

$\sqrt{(-\tfrac4{13}\cdot 3)^2 +(-\tfrac4{13}\cdot-1)^2 + (-\tfrac4{13}\cdot4^2)} =$ 'undefined'

Any help?

Answer 1

It's easier to do the calculation (in your head) without squaring and unsquaring the $-4/13$. The length is $$ \frac{4}{13}\sqrt{9 + 1 + 16} = \frac{4\sqrt{26}}{13} . $$

Answer 2

The last term should have the whole parenthesis squared, not just $4^2$.