Find the value of `lambda` , if four points with position vectors `3 hati + 6 hatj + 9 hatk, hati + 2 hatj + 3 hatk, 2 hati + 3 hatj + hatk and 4 hati + 6 hatj + lambdahat k` are coplanar.

Explanation

To find the value of \( \lambda \) such that the four points with given position vectors are coplanar, we can follow these steps:

### Step 1: Identify the position vectors
Let the position vectors of the points be:
- \( A = 3\hat{i} + 6\hat{j} + 9\hat{k} \)
- \( B = \hat{i} + 2\hat{j} + 3\hat{k} \)
- \( C = 2\hat{i} + 3\hat{j} + \hat{k} \)
- \( D = 4\hat{i} + 6\hat{j} + \lambda\hat{k} \)
...