Question

Let v:=(4,−2,−4) be a vector in R³.
Find a unit vector in the direction of v.

Answer 1

To find the unit vector in the direction of v = (4, -2, -4), first calculate the magnitude of v, which is 6, and then divide each component of v by this magnitude to get the unit vector u = (2/3, -1/3, -2/3).

Step-by-step explanation:

To find a unit vector in the direction of a given vector v = (4, -2, -4), we need to calculate the magnitude of v and then divide each component of v by this magnitude. The magnitude of v, denoted as |v|, is the square root of the sum of the squares of its components:

|v| = √(4² + (-2)² + (-4)²) = √(16 + 4 + 16) = √36 = 6.

Now, dividing each component of v by its magnitude gives the unit vector u:

u = (4/6, -2/6, -4/6) = (2/3, -1/3, -2/3).

Therefore, the unit vector in the direction of v is u = (2/3, -1/3, -2/3).