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.