Answered: |a|-|b| sin (ß- a) = = = b = (b1,b2) В…

|a|-|b| sin (ß- a) = = = b = (b1,b2) В P 8 a = (al,a2) |ab|(cos a sin 3 - sin a cos 3) al cos a b sin ß-a sin a b cos B a₁b₂-a₂b₁

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

I have these two formulas which are apparently to calculate the surface of the vectors, I don't get what the difference is between them, is it only the dimension? and could you please elaborate how they simplify the equations? thank you in advance

a b sin(3a)
=
=
b = (b1,b2)
В
P
a
a = (al,a2)
|ab|(cos a sin 3 - sin a cos 3)
al cos a b sin 3- a sin a b cos 3
a1b₂-a2b₁

(P)2
=
=
=
=
=
|a|2|b|2(sin 9)2
|a2|b|2 = \a|2|b|2(cos9)2
|a|2|b|2 = (a · b)2
(a + a + a)(b + b + bვ) → (ab + a2b2 + a3b3)2
(a2b3 − a3b2)2 + (a3bi — ab3)2 + (ab) — a2b1)2

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.

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