Question

(1 point) Rewrite the vector equation r(t)=(−1−2t)i+(5−5t)j+(3+4t)kr(t)=(−1−2t)i+(5−5t)j+(3+4t)k as the corresponding parametric equations for the line. x(t)=x(t)= y(t)=y(t)= z(t)=z(t)=

Answer 1

Answer:

x(t) = -1-2t

y(t) = 5-5t

z(t) = 3+4t

Explanation:

If you know the vector equation we can easily convert it to the parametric equation because we just need to rewrite the expression in terms of x,t,z of t:

r(t) = (−1−2t)i + (5−5t)j + (3+4t)k

x(t) = -1-2t

y(t) = 5-5t

z(t) = 3+4t

The important thing behind this concept is that you can represent a line in the space with a system of equations or with a vector notation and depending on what do you need to do you can change easily from one notation to the other. Note that the vector is made of a position vector (constant) and a direction vector in the direction of the line represented by the system of equations.