1. Let A=3a_y+5a_z, B=a_x-2a_y+4a_z, C=a_x+a_y-a_z. a-Find A.B, b-Find AxC and IAXC| c-Find C.AxB d-Find (AXC)xB e-Find a unit vector perpendicular to both B and C f-Find the vector component of A along B, A_B 2. Express the following vectors in rectangular coordinates: a- A rho sin(phi)a_rho+rho cos(phi)a_phi-3za_z b- c- Find A.B B=5rcos(phi)a_r+r^2a_theta+sin(theta)a_phi 3- Let r=xa_x+ya_y+za_z, describe the surface defined by the equations a- r.a_x+r.a_z=12 b- |rxa_y=3
1. Let A=3a_y+5a_z, B=a_x-2a_y+4a_z, C=a_x+a_y-a_z. a-Find A.B, b-Find AxC and IAXC| c-Find C.AxB d-Find (AXC)xB e-Find a unit vector perpendicular to both B and C f-Find the vector component of A along B, A_B 2. Express the following vectors in rectangular coordinates: a- A rho sin(phi)a_rho+rho cos(phi)a_phi-3za_z b- c- Find A.B B=5rcos(phi)a_r+r^2a_theta+sin(theta)a_phi 3- Let r=xa_x+ya_y+za_z, describe the surface defined by the equations a- r.a_x+r.a_z=12 b- |rxa_y=3
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:1. Let A=3a_y+5a_z, B=a_x-2a_y+4a_z, C=a_x+a_y-a_z.
a-Find A.B,
b-Find AxC and AxC|
c-Find C.AxB
d-Find (AXC)xB
e-Find a unit vector perpendicular to both B and C
f-Find the vector component of A along B, A_B
2. Express the following vectors in rectangular coordinates:
a-A=rho sin(phi)a_rho+rho cos(phi)a_phi-3za_z
b- B=5rcos (phi)a_r+r^2a_theta+sin(theta)a_phi
c- Find A.B
3- Let r=xa_x+ya_y+za_z, describe the surface defined by the equations
a- r.a_x+r.a_z=12
b- |rxa_y=3
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