Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k
parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t
Step-by-step explanation: The vector equation is a line of the form:
r = [tex]r_{0}[/tex] + t.v
where
[tex]r_{0}[/tex] is the position vector;
v is the vector;
For point (7,4,5):
[tex]r_{0}[/tex] = 7i + 4j + 5k
Then, the equation is:
r = 7i + 4j + 5k + t(3i + 2j - k)
r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k
The parametric equations of the line are of the form:
x = [tex]x_{0}[/tex] + at
y = [tex]y_{0}[/tex] + bt
z = [tex]z_{0}[/tex] + ct
So, the parametric equations are:
x = 7 + 3t
y = 4 + 2t
z = 5 - 5t
