Show that the straight lines whose direction cosines are given by the equations `a l+b m+c n=0` and `u l^2+vm^2+wn^2=0` are parallel or perpendicular as `(a^2)/u+(b^2)/v+(c^2)/w=0ora^2(v+w)+b^2(w+u)+c^2(u+v)=0.`

Explanation

To show that the straight lines whose direction cosines are given by the equations \( a l + b m + c n = 0 \) and \( u l^2 + v m^2 + w n^2 = 0 \) are parallel or perpendicular under the conditions \( \frac{a^2}{u} + \frac{b^2}{v} + \frac{c^2}{w} = 0 \) or \( a^2(v+w) + b^2(w+u) + c^2(u+v) = 0 \), we proceed as follows:

### Step 1: Write the Given Equations
We start with the two equations:
1. \( a l + b m + c n = 0 \) (Equation 1)
2. \( u l^2 + v m^2 + w n^2 = 0 \) (Equation 2)

### Step 2: Express \( l \) in Terms of \( m \) and \( n \)
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