3.17 Numerical Examples
87
Now,
A
2
2 + B
2
2 + C
2
2 =
(−0.00499)
2
+ (−0.009965)
2
+ (0.00562)
2
=
0.0125
∴ l 2 =
A 2
A
2
2 + B
2
2 + C
2
2
=
−0.00499
0.0125
= −0.399
m 2 =
B 2
A
2
2 + B
2
2 + C
2
2
=
−0.009965
0.0125
= −0.797
n 2 =
C 2
A
2
2 + B
2
2 + C
2
2
=
0.00562
0.0125
= 0.450
And for ε 3 = −0.126
(0.1 + 0.126)
0.15
−0.04
0.15
(−0.05 + 0.126)
0.05
−0.04
0.05
(0.05 + 0.126)
=
0.226 0.15 −0.04
0.15 0.076 0.05
−0.04 0.05 0.176
Now,
A 3 =
0.076 0.05
0.05 0.176
= 0.0134 − 0.0025 = 0.0109
B 3 = −
0.15 0.05
−0.04 0.176
= −(0.0264 + 0.002) = −0.0284
C 3 = −
0.15 0.076
−0.04 0.05
= 0.0075 + 0.00304 = 0.01054.
Now,
A
2
3 + B
2
3 + C
2
3 =
(0.0109)
2
+ (−0.0284)
2
+ (0.01054)
2
= 0.0322
∴ l 3 =
A 3
A
2
3 + B
2
3 + C
2
3
=
0.0109
0.0322
= 0.338
m 3 =
B 3
A
2
3 + B
2
3 + C
2
3
=
−0.0284
0.0322
= −0.882
n 3 =
C 3
A
2
3 + B
2
3 + C
2
3
=
0.01054
0.0322
= 0.327