Answer
$unit $, $a_1\vec i+a_2\vec j+a_3\vec k$, $\sqrt {a_1^2+a_2^2+a_3^2}$, $4\vec i-2\vec j+4\vec k$, $\langle 0, 7, -24 \rangle$
Work Step by Step
We can use two forms to represent a vector in three dimensions, in coordinate form or in terms of the $unit $ vectors i, j, and k as $\vec v=a_1\vec i+a_2\vec j+a_3\vec k$. To calculate the magnitude of a vector, we use the formula $|\vec v|=\sqrt {a_1^2+a_2^2+a_3^2}$. For vector $\langle 4, -2, 4 \rangle$ it is equivalent to
$4\vec i-2\vec j+4\vec k$, while for vector $7\vec j-24\vec k$, it is equivalent to $\langle 0, 7, -24 \rangle$
