In this question we have to convert Cartesian equation to vector equation, we are given with the Cartesian equation of the line which is as we can see that this line is not in the standard form, so after converting it we get,

Now the direction ratios of this line is 2,3,–6

The direction cosines of the line are,

l =

m =

n =

To convert this Cartesian form to the vector equation form, first equate the Cartesian form to a scalar,

= λ

Now equate all parts to this scalar individually,

x+2 = 2λ, y – = 3λ, z–5 = –6λ

x = 2λ–2, y = 3λ+, z = 5–6λ

we know that = x+y+z = +λ

x+y+z = (2λ–2) + (3λ+) + (–6λ+5)

x+y+z = (–2++5) + λ(2+3–6)

Therefore, the vector equation of the line is the mentioned above.