Question

What is the unit vector in the direction of? What is the unit vector in the direction of?

Short answer

The unit vector in the direction of.

The unit vector in the direction of .

Step-by-step solution

Definition of the unit vector

The unit vector in the direction of a vector is the vector divided by its magnitude, which is given by:

$\stackrel{\rightharpoonup }{r}=\frac{\stackrel{\rightharpoonup }{r}}{\left|\stackrel{\rightharpoonup }{r}\right|}$

Calculating unit vector for 2,2,2

Take the square root of the sum of the square of each component of the vector to obtain its magnitude,

$$\begin{gathered} =\sqrt{2^2+2^2+2^2} \\ =2\sqrt{3} \end{gathered}$$

Divide the vector by its magnitude to compute its unit vector,

Therefore, the unit vector in the direction of .

Calculating unit vector for 3,3,3

Take the square root of the sum of the square of each component of the vector to obtain its magnitude.

$$\begin{gathered} =\sqrt{3^3+3^3+3^3} \\ =3\sqrt{3} \end{gathered}$$

Divide the vector by its magnitude to compute its unit vector.

Therefore, the unit vector in the direction of .