Answers:
- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t>
- parametric equations:
x = 1 + 6t
y = -1 + 7t
z = 7 - 6t
Explanation:
To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,
v = q - p
= (7,6,1) - (1,-1,7)
v = (6, 7, -6)
The vector equation of the line is given by
Where
= a point in the line (we choose point p(1,-1,7))
So, the equation of the line joining p and q is given by
In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.
Since the vector equation is given by
The parametric equations of the line are given by:
- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t>
- parametric equations:
x = 1 + 6t
y = -1 + 7t
z = 7 - 6t
Explanation:
To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,
v = q - p
= (7,6,1) - (1,-1,7)
v = (6, 7, -6)
The vector equation of the line is given by
Where
So, the equation of the line joining p and q is given by
In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.
Since the vector equation is given by
The parametric equations of the line are given by: