Find the angle between the following pairs of lines:(i) ` -> r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)`and ` -> r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)`(ii) ` -> r=3 hat i+ hat j-2 hat k+lambda( hat i- hat j-2 hat k)`and ` -

Explanation

To find the angle between the given pairs of lines, we will use the formula for the angle between two lines represented in vector form. The angle \( \theta \) between two lines can be found using the dot product of their direction ratios.

### Given Lines:
1. Line 1:
\[ \mathbf{r_1} = 2\hat{i} - 5\hat{j} + \hat{k} + \lambda(3\hat{i} + 2\hat{j} + 6\hat{k}) \]
Direction ratios: \( \mathbf{b_1} = 3\hat{i} + 2\hat{j} + 6\hat{k} \)
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