Consider the following theorem. If a, b, and c are vectors and c is a scalar, then we have the following properties of the cross product. 1. ax b = -bxa 2. (ca) x b = c(a x b) = ax (cb) 3. ax (b + c) = axb + axc 4. (a + b) x c = axc + bxc 5. a (b x c) = (axb) c 6. ax (bx c) = (a c)b (a b)c Prove the property a x b = -b x a of the given theorem. Let a = (a₁, a2, a 3) and b = (b₁,b₂, b3). Then we get the following. axb = = (-1) = -bxa.
Consider the following theorem. If a, b, and c are vectors and c is a scalar, then we have the following properties of the cross product. 1. ax b = -bxa 2. (ca) x b = c(a x b) = ax (cb) 3. ax (b + c) = axb + axc 4. (a + b) x c = axc + bxc 5. a (b x c) = (axb) c 6. ax (bx c) = (a c)b (a b)c Prove the property a x b = -b x a of the given theorem. Let a = (a₁, a2, a 3) and b = (b₁,b₂, b3). Then we get the following. axb = = (-1) = -bxa.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:Consider the following theorem.
If a, b, and c are vectors and c is a scalar, then we have the following properties of the cross product.
1. ax b = -bxa
2. (ca) x b = c(a x b) = ax (cb)
3. ax (b + c) = axb + ax c
4. (a + b) x c = axc + bxc
5. a (b x c) = (axb).c
6. ax (bx c) = (a c)b (a b)c
Prove the property a x b = -b x a of the given theorem.
Let a = (a₁, a2, a 3) and b = (b₁,b₂, b3). Then we get the following.
axb=
=
(-1)
= -bxa.
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