Multivariable Calculus Quiz
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VECTORS AND GEOMETRY IN 3D
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Consider the line
L
L
L
given by the symmetric equations
x
−
3
2
=
y
+
1
−
1
=
z
−
5
4
\frac{x-3}{2} = \frac{y+1}{-1} = \frac{z-5}{4}
2
x
−
3
=
−
1
y
+
1
=
4
z
−
5
. Which of the following lines is parallel to
L
L
L
and passes through the origin?
A
r
⃗
=
t
⟨
2
,
−
1
,
4
⟩
\vec{r} = t\langle 2, -1, 4 \rangle
r
=
t
⟨
2
,
−
1
,
4
⟩
B
x
3
=
y
−
1
=
z
5
\frac{x}{3} = \frac{y}{-1} = \frac{z}{5}
3
x
=
−
1
y
=
5
z
C
r
⃗
=
t
⟨
1
,
−
2
,
2
⟩
\vec{r} = t\langle 1, -2, 2 \rangle
r
=
t
⟨
1
,
−
2
,
2
⟩
D
x
1
=
y
+
1
−
2
=
z
2
\frac{x}{1} = \frac{y+1}{-2} = \frac{z}{2}
1
x
=
−
2
y
+
1
=
2
z
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