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 unit vector

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

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

Calculating unit vector for 2,2,2

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

$\sqrt{2^2+2^2+2^2}=2\sqrt{3}$

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

$\sqrt{3^2+3^2+3^2}=3\sqrt{3}$

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