Write the value of `p` for which ` vec a=3 hat i+2 hat j+9 hat k\ a n d\ vec b= hat i+p hat j+3 hat k` are parallel vectors.

Explanation

To find the value of \( p \) for which the vectors \( \vec{a} = 3 \hat{i} + 2 \hat{j} + 9 \hat{k} \) and \( \vec{b} = \hat{i} + p \hat{j} + 3 \hat{k} \) are parallel, we can follow these steps:

### Step 1: Understand the condition for parallel vectors
Two vectors \( \vec{a} \) and \( \vec{b} \) are parallel if one is a scalar multiple of the other. This means we can write:
\[ \vec{b} = \lambda \vec{a} \]
for some scalar \( \lambda \).
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