Answer
< $\frac{3}{35}$, $\frac{-1}{35}$, $\frac{-1}{7}$>
Work Step by Step
Note: The vectors can be rewritten using <>, so
w = <3, -1, -5>
To solve $\frac{1}{ w∙w}$ * w, there are multiple steps to take.
First, find the dot product of w∙w. Taking the dot product produces a scalar. The dot product can be formed by multiplying the first components of the vector together, multiplying the second components of the vector together, multiplying the third components of the vector together, and adding all the products together.
1. Multiply the first components together: 3 * 3 = 9
2. Multiply the second components together: -1 * -1 = 1
3. Multiply the third components together: -5 * -5 = 25
4. Add the products together: 9 + 1 + 25 = 35
The dot product is 35.
Since the vector w is multiplied by 1/w∙w, we will multiply each component of the vector w by 1/35.
1. Multiply the first component by 1/35: (1/35) * 3 = $\frac{3}{35}$
2. Multiply the second component by 1/35: (1/35) * -1 = $\frac{-1}{35}$
3. Multiply the third component by 1/35: (1/35) * -5 = -5/35 = $\frac{-1}{7}$
The vector can be rewritten as < $\frac{3}{35}$, $\frac{-1}{35}$, $\frac{-1}{7}$>.
