Can you find two vectors in R whose dot product is equal to their cross product? No, because the cross product is a scalar, while the dot product is a vector Yes, but only if the two original vectors are identical to one another No, because the dot product is in R while the cross product is in R³ Yes, but at least one of the vectors must be the zero vector
Can you find two vectors in R whose dot product is equal to their cross product? No, because the cross product is a scalar, while the dot product is a vector Yes, but only if the two original vectors are identical to one another No, because the dot product is in R while the cross product is in R³ Yes, but at least one of the vectors must be the zero vector
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:If e is the standard alternating tensor and 8 is the Kronecker delta, then
Ejkl
O Eijkdkm = Emij
Eijk
-Ekij
%3D
Sik
%3D
Eijk – Ejki
If e is the standard alternating (rank-3) tensor and a is a vector in R3, then
Eijkak represents
A rank-2 tensor (a matrix)
A rank-0 tensor (a scalar)
A rank-3 tensor
A rank-1 tensor (a vector)
Transcribed Image Text:Can you find two vectors in R³ whose dot product is equal to their cross product?
No, because the cross product is a scalar, while the dot product is a vector
Yes, but only if the two original vectors are identical to one another
O No, because the dot product is in R while the cross product is in R³
Yes, but at least one of the vectors must be the zero vector
Let a and b be vectors in R3. Then,
Ja x b| gives the volume of the parallelepiped generated from the vectors a
and b.
a x b and b are orthogonal.
|a – b| is the vector pointing from the point with position vector þ to the
point with position vector a.
|a· b| gives the area of the parallelogram generated from the vectors a and b
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