Final answer:
A coordinate line passing through (-3,-6,6) towards the direction of the unit vector ĵ in three-dimensional space can be described by the parametric equations x = -3, y = -6 + t, and z = 6, where t is a parameter denoting position along the line.
Step-by-step explanation:
When considering the coordinate line that passes through (-3,-6,6) and moves towards the direction of the unit vector ĵ, which points vertically upward, we're talking about a line in three-dimensional space.
In three-dimensional space, we can represent a line with a base point and a direction vector. The base point is given as (-3,-6,6). Since we want the line to move towards ĵ, our direction vector will simply be (0, 1, 0), where the 1 indicates movement in the positive y-direction, and the other components are zero because there's no movement along the x or z axis.
To write an equation for this line, we consider the vector format L(t) = R0 + tV, where R0 is the base point, V is the direction vector, and t is a parameter. For our specific case, the line equation becomes L(t) = (-3,-6,6) + t(0,1,0), which simplifies to a parametric form of x = -3, y = -6 + t, z = 6.