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A line is given by r = (2î - ĵ + 3k̂) + λ(4î + 5ĵ… | StemPy Lab
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A line is given by r = (2î - ĵ + 3k̂) + λ(4î + 5ĵ - 2k̂). Which of these is the same line in Cartesian form?
Mathematics
Easy
High School (11–12)
Vectors and Three-Dimensional Geometry › Three-Dimensional Geometry
A-Level
IB
Created by
StemPy Lab
A line is given by
r
⃗
=
(
2
i
^
−
j
^
+
3
k
^
)
+
λ
(
4
i
^
+
5
j
^
−
2
k
^
)
\vec{r} = (2\hat{i} - \hat{j} + 3\hat{k}) + \lambda(4\hat{i} + 5\hat{j} - 2\hat{k})
r
=
(
2
i
^
−
j
^
+
3
k
^
)
+
λ
(
4
i
^
+
5
j
^
−
2
k
^
)
. Which of these is the same line in Cartesian form?
x
−
4
2
=
y
−
5
−
1
=
z
+
2
3
\dfrac{x - 4}{2} = \dfrac{y - 5}{-1} = \dfrac{z + 2}{3}
2
x
−
4
=
−
1
y
−
5
=
3
z
+
2
x
−
2
4
=
y
+
1
5
=
z
−
3
−
2
\dfrac{x - 2}{4} = \dfrac{y + 1}{5} = \dfrac{z - 3}{-2}
4
x
−
2
=
5
y
+
1
=
−
2
z
−
3
x
−
2
4
=
y
−
1
5
=
z
−
3
2
\dfrac{x - 2}{4} = \dfrac{y - 1}{5} = \dfrac{z - 3}{2}
4
x
−
2
=
5
y
−
1
=
2
z
−
3
x
+
2
4
=
y
−
1
5
=
z
+
3
−
2
\dfrac{x + 2}{4} = \dfrac{y - 1}{5} = \dfrac{z + 3}{-2}
4
x
+
2
=
5
y
−
1
=
−
2
z
+
3
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