Find the angle between the vectors whose direction cosines are proportional to `2,3,-6` and `3,-4,5.`

Explanation

To find the angle between the vectors whose direction cosines are proportional to `2, 3, -6` and `3, -4, 5`, we can follow these steps:

### Step 1: Identify the direction ratios
Let the direction ratios of the first vector be \( L_1 = 2, M_1 = 3, N_1 = -6 \) and for the second vector \( L_2 = 3, M_2 = -4, N_2 = 5 \).

### Step 2: Use the formula for the cosine of the angle between two vectors
The cosine of the angle \( \theta \) between two vectors can be calculated using the formula:
\[
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