How do you normalize ( i + 7 j + 4 k )?

Mar 8, 2016

The normalized vector is the unit vector form to you vector, thus:
$\vec{u} = \frac{1}{\sqrt{66}} \left(i + 7 j + 4 k\right)$

Explanation:

Normalization implies finding the unit vector expression to you vector quantity. So given you vector:
$\vec{v} = i + 7 j + 4 k$ the unit vector is:
vec(u) = 1/|vec(v)| vec(v); |vec(v)| = sqrt(1 + 49 + 16) = sqrt(66)
$\vec{u} = \frac{1}{\sqrt{66}} \left(i + 7 j + 4 k\right)$
Your vector can be written as:
$\vec{v} = | \vec{v} | \vec{u} = \sqrt{66} \vec{u}$