Answer:
The vector equation of the line is and parametric equations for the line are
,
,
.
Step-by-step explanation:
It is given that the line passes through the point (0,11,-8) and parallel to the line
The parametric equation are defined as
Where, (x₁,y₁,z₁) is point from which line passes through and <a,b,c> is cosine of parallel vector.
From the given parametric equation it is clear that the line passes through the point (-1,6,3) and parallel vector is <4,-4,6>.
The required line is passes through the point (0,11,-8) and parallel vector is <4,-4,6>. So, the parametric equations for the line are
Vector equation of a line is
where, is a position vector and
is cosine of parallel vector.
Therefore the vector equation of the line is and parametric equations for the line are
,
,
.