Find the values `p` so that line `(1-x)/3=(7y-14)/(2p)=(z-3)/2a n d(7-7x)/(3p)=(y-5)/1=(6-z)/5` are at right angles.

Explanation

To find the values of \( p \) such that the given lines are at right angles, we can follow these steps:

### Step 1: Write the equations of the lines in standard form
The given equations of the lines can be expressed in the standard form \( \frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c} \).

For the first line:
\[
\frac{1 - x}{3} = \frac{7y - 14}{2p} = \frac{z - 3}{2}
...