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A line passes through (1, 0, 2) with direction ratios… | StemPy Lab
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A line passes through (1, 0, 2) with direction ratios (2, 1, -1). A second line passes through (0, 2, 1) with direction ratios (1, -1, 3). What is the value of (a₂ - a₁) · (b₁ × b₂), and what does it show?
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High School (11–12)
Vectors and Three-Dimensional Geometry › Three-Dimensional Geometry
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Created by
StemPy Lab
A line passes through
(
1
,
0
,
2
)
(1, 0, 2)
(
1
,
0
,
2
)
with direction ratios
(
2
,
1
,
−
1
)
(2, 1, -1)
(
2
,
1
,
−
1
)
. A second line passes through
(
0
,
2
,
1
)
(0, 2, 1)
(
0
,
2
,
1
)
with direction ratios
(
1
,
−
1
,
3
)
(1, -1, 3)
(
1
,
−
1
,
3
)
. What is the value of
(
a
⃗
2
−
a
⃗
1
)
⋅
(
b
⃗
1
×
b
⃗
2
)
(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2)
(
a
2
−
a
1
)
⋅
(
b
1
×
b
2
)
, and what does it show?
5
5
5
, so the lines are skew
0
0
0
, so the lines intersect
−
13
-13
−
13
, so the lines intersect
−
13
-13
−
13
, so the lines are skew
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