a. Show that cos α = |v| cos B = b V cos Y = ਵਿਚ and cos²a+ cos²3 + cos²y = 1. These cosines are called the direction cosines of V. b. Unit vectors are built from direction cosines Show that if v = ai + bj + ck is a unit vector, then a, b, and c are the direction cosines of V.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The direction angles a,B,Y of a vector v=ai+bj+ck
 are defined as follows:

a is the angle between v and the positive x-axis 
B is the angle between v and the positive y-axis 
Y is the angle between v and the positive z-axis 

 

a. Show that
Cos α =
|v|
cos B =
b
V
cos Y =
ਵਿਚ
and cos²a + cos²3 + cos²y = 1. These cosines are called the direction
cosines of V.
b. Unit vectors are built from direction cosines Show that if
v = ai + bj + ck is a unit vector, then a, b, and c are the direction cosines
of V.
Transcribed Image Text:a. Show that Cos α = |v| cos B = b V cos Y = ਵਿਚ and cos²a + cos²3 + cos²y = 1. These cosines are called the direction cosines of V. b. Unit vectors are built from direction cosines Show that if v = ai + bj + ck is a unit vector, then a, b, and c are the direction cosines of V.
x
>
B
Transcribed Image Text:x > B
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