Given: Vector A = 3î + 2j and Vector B = 2î + 3j - k

To find: Unit vector along (Ā-B)

Solution:

Step 1: Find the vector (Ā-B)
We know that (Ā-B) = A - B
So, (Ā-B) = (3î + 2j) - (2î + 3j - k)
Simplifying (Ā-B), we get (Ā-B) = î - j + k

Step 2: Find the magnitude of (Ā-B)
Magnitude of (Ā-B) is given by |Ā-B| = sqrt(1^2 + (-1)^2 + 1^2)
|Ā-B| = sqrt(3)

Step 3: Find the unit vector along (Ā-B)
Unit vector along (Ā-B) is given by [(Ā-B)/|Ā-B|]
So, [(Ā-B)/|Ā-B|] = (î - j + k)/sqrt(3)

Therefore, the unit vector along (Ā-B) is (î - j + k)/sqrt(3).

Explanation:

To find the unit vector along (Ā-B), we need to follow three steps. Firstly, we need to find the vector (Ā-B). Secondly, we need to find the magnitude of the vector (Ā-B). Finally, we need to divide the vector (Ā-B) by its magnitude to get the unit vector along (Ā-B).

In the given question, we have two vectors A and B. By subtracting vector B from vector A, we get the vector (Ā-B). By simplifying the equation, we get the vector (Ā-B) = î - j + k.

To find the magnitude of (Ā-B), we need to calculate the square root of the sum of the squares of the coefficients of the vector (Ā-B). We get the magnitude of (Ā-B) as sqrt(3).

Finally, to get the unit vector along (Ā-B), we need to divide the vector (Ā-B) by its magnitude. We get the unit vector along (Ā-B) as (î - j + k)/sqrt(3).

Therefore, the unit vector along (Ā-B) is (î - j + k)/sqrt(3).