Vector problem?

Let V₁ = ai + bj
Since V₁ is parallel to W, a/-2 = b/1
Then, a = -2b
Hence, V₁ = -2bi + bj

Let V₂ = ci + dj
Since V₂ is orthogonal to W, V₂•W = 0
Then, (ci + dj)•(-2i + j) = 0
-2c + d = 0
d = 2c
Hence, V₂ = ci + 2cj

Decompose V into V₁ and V₂:
V₁ + V₂ = V
(-2bi + bj) + (ci + 2cj) = 3i + j
(-2b + c)i + (b + 2c)j = 3i + j

-2b + c = 3 …… [1]
b + 2c = 1 …… [2]

[1] + [2]*2:
5c = 5
c = 1

[2] - [1]*2:
5b = -5
b = -1

The answers:
V₁ = 2i - j
V₂ = 1 + 2j