Show that the straight lines whose direction cosines are given by the equations `al+bm+cn=0` and `u l^2+z m^2=v n^2+w n^2=0` are parallel or perpendicular as `a^2/u+b^2/v+c^2/w=0` or `a^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 \( al + bm + cn = 0 \) and \( ul^2 + vm^2 + wn^2 = 0 \) 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 can follow these steps:

### Step 1: Understand the Direction Cosines
The first equation \( al + bm + cn = 0 \) represents a plane in three-dimensional space, where \( l, m, n \) are the direction cosines of a line. The second equation \( ul^2 + vm^2 + wn^2 = 0 \) represents another condition involving the direction cosines.

**Hint:** Recall that direction cosines are the cosines of the angles that a line makes with the coordinate axes.

### Step 2: Rearranging the First Equation
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