Write a vector equation AND parametric equations of the line through the points A(6,-1,5) and B(-2,-3,6)
direction vector = [8,2,-1]
a vector equation
r = (6,-1,5) + t(8,2,-1)
use that to write the parametrics
how do i write parametrics
since you have
r = (6,-1,5) + t(8,2,-1), which is correct we can say
x = 6 = 8t
y = -1 + 2t
z = 5 - t
To write the parametric equations of the line through points A(6,-1,5) and B(-2,-3,6) using the given direction vector [8,2,-1], you can represent the position vector r as the sum of the initial point A and the direction vector scaled by a parameter t.
The vector equation is:
r = (6, -1, 5) + t(8, 2, -1)
To express it in parametric form, you can write each component of the position vector r as a separate equation:
x = 6 + 8t
y = -1 + 2t
z = 5 - t
These equations express the x, y, and z coordinates of any point on the line as functions of the parameter t. By varying the value of t, you can obtain different points on the line.