Question

A parameterization of the line segment from (-3,-3,-3) to (0,0,0) is
Select one:
a. r(t)=⟨3t,3t,3t⟩
for t∈[−3,0]
.

b. r(t)=⟨t,−t,t⟩
for t∈[−3,0]
.

c. r(t)=⟨t,t,t⟩
for t∈[−3,0]
.
d. r(t)=⟨t,t⟩
for t∈[0,3]
.

e. r(t)=⟨t,t,t⟩
for t∈[−3,3].

Answer 1

Let $r(t)$ be parametrization for $t\in [a,b].$

We know that $r(a)=(-3,-3,-3), \ r(b)=(0,0,0)$ .

a. $r(-3)=(-9,-9-9), \ r(0)=(0,0,0)$

b. $r(-3)=(-3,3,-3), \ r(0)=(0,0,0)$

c. $r(-3)=(-3,-3,-3), \ r(0)=(0,0,0)$

d. $r(0)=(0,0), \ r(3)=(3,3)$

e. $r(-3)=(-3,-3,-3), \ r(3)=(3,3,3)$

Answer: c.