The direction ratios of the line x – y + z – 5 = 0 = x – 3y – 6 are proportional to

We have,

x – y + z – 5 = 0 = x – 3y – 6

→ x – y + z – 5 = 0

x – 3y – 6 = 0

→ x – y + z – 5 = 0 → (1)

x = 3y + 6 → (2)

From (1) and (2) we get,

3y + 6 – y + z – 5 = 0

2y + z + 1 = 0

y

Also, y → From (2)

So, the given equation can be re-written as

Hence the direction ratios of the given line are proportional to 3,1,-2.