Find the angle between the planes whose vector equations are ` vec r.(2 hat i+2 hat j-3 hat k)=5`and ` vec r.(3 hat i-3 hat j+5 hat k)=3`.

Explanation

To find the angle between the two planes given by their vector equations, we can follow these steps:

### Step 1: Identify the normal vectors of the planes
The vector equations of the planes are given as:
1. \(\vec{r} \cdot (2\hat{i} + 2\hat{j} - 3\hat{k}) = 5\)
2. \(\vec{r} \cdot (3\hat{i} - 3\hat{j} + 5\hat{k}) = 3\)

From these equations, we can identify the normal vectors of the planes:
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