If `veca=2 hat i+2 hat j+3 hat k , vecb=- hat i+2 hat j+ hat k`and ` vecc=3 hat i+ hat j```are such that ` veca+lambda vecb```is perpendicular to `vecc`, then find the value of `lambda`.

Explanation

To solve the problem, we need to find the value of \( \lambda \) such that \( \vec{a} + \lambda \vec{b} \) is perpendicular to \( \vec{c} \).

Given:
- \( \vec{a} = 2\hat{i} + 2\hat{j} + 3\hat{k} \)
- \( \vec{b} = -\hat{i} + 2\hat{j} + \hat{k} \)
- \( \vec{c} = 3\hat{i} + \hat{j} \)

### Step 1: Write the expression for \( \vec{a} + \lambda \vec{b} \)
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