MATH SOLVE

4 months ago

Q:
# The normal of the vector: (2,-2,4) is equal to 2β6 ?

Accepted Solution

A:

To find the normal (or the unit normal) of a vector, you need to normalize the vector, which means dividing each component of the vector by its magnitude. The magnitude of a vector (a, b, c) is given by the formula:
Magnitude = β(aΒ² + bΒ² + cΒ²)
In your case, the vector is (2, -2, 4), so:
a = 2
b = -2
c = 4
Magnitude = β(2Β² + (-2)Β² + 4Β²) = β(4 + 4 + 16) = β24 = 2β6
Now, to find the unit normal, you divide each component of the vector by its magnitude:
Unit Normal = (2/2β6, -2/2β6, 4/2β6) = (1/β6, -1/β6, 2/β6)
So, the unit normal of the vector (2, -2, 4) is indeed (1/β6, -1/β6, 2/β6), and not just 2β6.