What is the relationship between the volume of thetetrahedron defined by the vectors [ a 1 a 2 1 ] , [ b 1 b 2 1 ] , [ c 1 c 2 1 ] and the area of the triangle with vertices [ a 1 a 2 ] , [ b 1 b 2 ] , [ c 1 c 2 ] ? See Exercises 4 and 5. Explain this relationship geometrically. Hint: Consider the top face of the tetrahedron.
What is the relationship between the volume of thetetrahedron defined by the vectors [ a 1 a 2 1 ] , [ b 1 b 2 1 ] , [ c 1 c 2 1 ] and the area of the triangle with vertices [ a 1 a 2 ] , [ b 1 b 2 ] , [ c 1 c 2 ] ? See Exercises 4 and 5. Explain this relationship geometrically. Hint: Consider the top face of the tetrahedron.
Solution Summary: The author calculates the relationship between the volume of the given tetrahedron and triangle.
What is the relationship between the volume of thetetrahedron defined by the vectors
[
a
1
a
2
1
]
,
[
b
1
b
2
1
]
,
[
c
1
c
2
1
]
and the area of the triangle with vertices
[
a
1
a
2
]
,
[
b
1
b
2
]
,
[
c
1
c
2
]
? See Exercises 4 and 5. Explain this relationship geometrically. Hint: Consider the top face of the tetrahedron.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.