1 Properties of the Cross Product: lamat, 1.) ||lox b|| = |lo||-·||bl| - sind, where O & [alt] is the angle between a and b. 2.) axb la, axb1b, and the triple (a, b, axb) obeys the right -hand rule, 3 axb-bxa 4. axb=0 iff of the other." а one of the vectors a and b is a scalar multiple gods 5. ax (btc) = a + b + axc ах (6₁) (a+b) = c = ax c + bxc 7₁) (α. a) xb = α (axb) = f(ab), EIR
1 Properties of the Cross Product: lamat, 1.) ||lox b|| = |lo||-·||bl| - sind, where O & [alt] is the angle between a and b. 2.) axb la, axb1b, and the triple (a, b, axb) obeys the right -hand rule, 3 axb-bxa 4. axb=0 iff of the other." а one of the vectors a and b is a scalar multiple gods 5. ax (btc) = a + b + axc ах (6₁) (a+b) = c = ax c + bxc 7₁) (α. a) xb = α (axb) = f(ab), EIR
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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Question
![12 Properties of the Cross Product: tand
1.) ||ox b|| = llall ·||bl| -sind, where O & [OITT] is the ongle
between
a
and b.
2.) axbla, axb¹1b, and the triple (a,b, axb) obeys the right
- hand rule,
33 axb-bra
4.) axb=0 iff
of the other.
one
of the vectors a and b is a scalar multiple
5. ax (btc) = a+b+axc
ах
(6₁) (a+b) = ( = 0+<+b+c
(7₁) (α. a) xb - α (axb)= a =(ab), αEIR
Prove each one: -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dbb4ae4-0d65-4baa-9481-63f79be91eca%2F96f7fcc5-91b7-4b4b-beb3-4523108b1301%2Fmzf3nh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12 Properties of the Cross Product: tand
1.) ||ox b|| = llall ·||bl| -sind, where O & [OITT] is the ongle
between
a
and b.
2.) axbla, axb¹1b, and the triple (a,b, axb) obeys the right
- hand rule,
33 axb-bra
4.) axb=0 iff
of the other.
one
of the vectors a and b is a scalar multiple
5. ax (btc) = a+b+axc
ах
(6₁) (a+b) = ( = 0+<+b+c
(7₁) (α. a) xb - α (axb)= a =(ab), αEIR
Prove each one: -
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