A

Step 1: Identify the vectors given in the question. The vectors are:
**A = 2i + 2j + k** and **B = i + 6j + 2k**.

Step 2: To find the projection of vector A along vector B, we use the formula:
$$ ext{Projec}_{B}(A) = \frac{A \cdot B}{B \cdot B} B$$

Step 3: Calculate the dot product $A \cdot B$:
$$A \cdot B = (2)(1) + (2)(6) + (1)(2) = 2 + 12 + 2 = 16$$

Step 4: Calculate the dot product $B \cdot B$:
$$B \cdot B = (1)(1) + (6)(6) + (2)(2) = 1 + 36 + 4 = 41$$

Step 5: Substitute these values back into the projection formula:
$$ ext{Projec}_{B}(A) = \frac{16}{41} B$$
$$= \frac{16}{41}(i + 6j + 2k) = \frac{16}{41}i + \frac{96}{41}j + \frac{32}{41}k$$

Therefore, the projection of vector A along vector B is **(i) and (ii)** would have a similar procedure with respective vectors.