Vectores

VECTOR A
IAI= 1.82m
Ax=IAI cos θ
Ax= 1.82m cos 108°= -.56m
Ay=IAI sen θ IAIAx
Ay= 1.82m sen 108°= 1.73m Ay θ=108°



VECTOR B
Bx= 4.57m
By=-.91m
Bz= -8.22mIBI=√(Bx)²+(By)²+(Bz)²
IBI=√(4.57)²+(-.97)²+(-8.22)²
IBI= 9.35 m

VECTOR C
Cx= ICI cos αCx= 22.86 cos 152°= -13.11m
Cy= ICI cos β
Cy= 22.86 cos 40°= 17.51m
Cz= ICI cos γ Y
Cz= 22.86 cos 288°= 7.06m




VECTOR D
Dx= IDI cos θ
IDI= Dx ÷ cos θIDI= -8 ÷ cos 340° θ=340°
IDI= -8.5m
Dx= 8m
Dy= IDI sen θ
Dy= -8.5 sen 340°=2.9m

Rx= -.56 + 4.57 - 13.11 - 7.9= - 17m
Ry= 1.73 - .91 + 17.51 + 2.9= 21.23m
Rz= - 8.22 + 7.06= - 1.16m
IRI=√(Rx)²+(Ry)²+(Rz)²
IRI=√(-17)²+(21.23)²+(-1.16)²
IRI=27.22m Z




α= cos¯¹(-17÷27.22)= 128.64°
β=cos¯¹(21.23÷27.22)= 38.74°
γ= cos¯¹(-1.16÷27.22)= 29.44°

R= A+B+C+D+E
E= R-A-B-C-D
Ex= 2 – (-.56) – (4.57) – (-13.11) –(-8) = 19.1m
Ey= 1 –(1.73) – (-.91) – (17.51) – (9.2) = - 26.53mEz= 8 – (-8.22) – (7.06) = 9.16m
IEI=√(19.1)²+(-26.53)²+(9.16)²
IEI= 33.49m IEI


IA•BI
IA•BI=AxBx+AyBy+AzBz
IA•BI= (-.56)(4.57)+(1.73)(-.91)+(0)(-8.22)= - 4.1335m
IAI IBI cosΦ = AxBx+AyBy+AzBz IAI
Φ= cos¯¹ (AxBx+AyBy+AzBz ÷ IAI IBI )
Φ= cos¯¹(-4.1335 ÷ 17.01)= 104.06°