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Practice Question: Cross Product and Volume
Related Topics
Wize University Linear Algebra Textbook > Products of Vectors
Volume of a Parallelepiped (Triple Product)
3 Activities
Practice Question: Application of Cross Product
Find the volume of the parallelepiped defined by the vectors
u
⃗
=
(
1
,
2
,
0
)
,
v
⃗
=
(
0
,
3
,
1
)
\vec{u}=\left(1,2,0\right),\ \vec{v}=\left(0,3,1\right)
u
=
(
1
,
2
,
0
)
,
v
=
(
0
,
3
,
1
)
and
w
⃗
=
(
1
,
1
,
5
)
\vec{w}=\left(1,1,5\right)
w
=
(
1
,
1
,
5
)
.
Answer
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Check Submission
More Volume of a Parallelepiped (Triple Product) Questions:
Practice Question: Cross Product and Volume
Practice Question: Application of Cross Product
Find the volume of the parallelepiped defined by the vectors
u
⃗
=
(
1
,
2
,
0
)
,
v
⃗
=
(
0
,
3
,
1
)
\vec{u}=\left(1,2,0\right),\ \vec{v}=\left(0,3,1\right)
u
=
(
1
,
2
,
0
)
,
v
=
(
0
,
3
,
1
)
and
w
⃗
=
(
1
,
1
,
5
)
\vec{w}=\left(1,1,5\right)
w
=
(
1
,
1
,
5
)
.
133 - FML 3 - 18.1W e.g. 39.2
Consider the points
P
1
=
(
1
,
4
,
1
)
\bcb{P_1 = (1,4,1)}
P
1
=
(
1
,
4
,
1
)
,
P
2
=
(
3
,
4
,
−
1
)
\bcb{P_2 = (3,4,-1)}
P
2
=
(
3
,
4
,
−
1
)
,
P
3
=
(
2
,
4
,
−
2
)
\bcb{P_3 = (2,4,-2)}
P
3
=
(
2
,
4
,
−
2
)
,
P
4
=
(
0
,
2
,
0
)
\bcb{P_4 = (0,2,0)}
P
4
=
(
0
,
2
,
0
)
.
Find the volume of the parallelepiped defined by the vectors
P
1
P
2
⃗
\bcb{\vec{P_1P_2}}
P
1
P
2
,
P
1
P
3
⃗
\bcb{\vec{P_1P_3}}
P
1
P
3
and
P
1
P
4
⃗
\bcb{\vec{P_1P_4}}
P
1
P
4
.
$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | 133 - FML 3 - 18.1W e.g. 39.2_$\tkcth{Mock F}\tkct{?}$_$\tkct{no soln / vid}$
Consider the points
P
1
=
(
1
,
4
,
1
)
\bcb{P_1 = (1,4,1)}
P
1
=
(
1
,
4
,
1
)
,
P
2
=
(
3
,
4
,
−
1
)
\bcb{P_2 = (3,4,-1)}
P
2
=
(
3
,
4
,
−
1
)
,
P
3
=
(
2
,
4
,
−
2
)
\bcb{P_3 = (2,4,-2)}
P
3
=
(
2
,
4
,
−
2
)
,
P
4
=
(
0
,
2
,
0
)
\bcb{P_4 = (0,2,0)}
P
4
=
(
0
,
2
,
0
)
.
Find the volume of the parallelepiped defined by the vectors
P
1
P
2
⃗
\bcb{\vec{P_1P_2}}
P
1
P
2
,
P
1
P
3
⃗
\bcb{\vec{P_1P_3}}
P
1
P
3
and
P
1
P
4
⃗
\bcb{\vec{P_1P_4}}
P
1
P
4
.
Find the volume of the parallelepiped determined by
𝑢
⃗
=
(
1
,
3
,
3
)
,
𝑣
⃗
=
(
1
,
0
,
2
)
,
𝑢⃗ = (1,3,3), \vec𝑣 = (1,0,2),
u
⃗
=
(
1
,
3
,
3
)
,
v
=
(
1
,
0
,
2
)
,
and
𝑤
⃗
=
(
0
,
2
,
3
)
.
𝑤⃗= (0,2,3).
w
⃗
=
(
0
,
2
,
3
)
.
Additional practice problems--vector products
Additional Practice Problems--Vector Products
1. If
u
⃗
=
(
−
2
,
3
,
−
1
)
,
v
⃗
=
(
−
1
,
−
2
,
3
)
\vec{u}=\left(-2,3,-1\right),\ \ \vec{v}=\left(-1,-2,3\right)
u
=
(
−
2
,
3
,
−
1
)
,
v
=
(
−
1
,
−
2
,
3
)
, find
a)
u
⃗
∙
v
⃗
\vec{u}\ \bullet\ \vec{v}
u
∙
v
Find the volume of the parallelepiped defined by the vectors
u
→
=
(
1
,
0
,
1
)
\overrightarrow{u}=\left(1,0,1\right)
u
=
(
1
,
0
,
1
)
,
v
→
=
(
2
,
−
1
,
0
)
\overrightarrow{v}=\left(2,-1,0\right)
v
=
(
2
,
−
1
,
0
)
and
w
→
=
(
3
,
−
3
,
4
)
\overrightarrow{w}=\left(3,-3,4\right)
w
=
(
3
,
−
3
,
4
)
.