Find the angle between the following pair of lines whose direction ratios are given -1,2,1and 2,3,-1

Explanation

To find the angle between the two lines given their direction ratios, we can use the formula for the cosine of the angle between two lines in three-dimensional space. The direction ratios of the lines are given as:

Line 1: \( (-1, 2, 1) \)
Line 2: \( (2, 3, -1) \)

### Step 1: Identify the direction ratios
Let:
- \( a_1 = -1 \), \( b_1 = 2 \), \( c_1 = 1 \) (for Line 1)
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