1. Find DirectionCosines(A)
`A=(1,2,2)`,`C=(1,2,2)`
Solution:
Here `vec A=(1,2,2),vec B=(2,2,1),vec C=(1,2,2)`
1. Calculate the magnitude(length) of vector `vec A`
`|vec A|`
`=sqrt(A_1^2 + A_2^2 + A_3^2)`
`=sqrt(1^2 + 2^2 + 2^2)`
`=sqrt(1 + 4 + 4)`
`=sqrt(9)`
`=3`
2. Calculate the direction cosines of vector `vec A`
`cos alpha=(A_1)/(|vec A|)=1/3=0.3333`
`cos beta=(A_2)/(|vec A|)=2/3=0.6667`
`cos gamma=(A_3)/(|vec A|)=2/3=0.6667`
2. Find DirectionCosines(A)
`A=(3,4)`,`C=(3,4)`
Solution:
Here `vec A=(3,4),vec B=(4,3),vec C=(3,4)`
1. Calculate the magnitude(length) of vector `vec A`
`|vec A|`
`=sqrt(A_1^2 + A_2^2)`
`=sqrt(3^2 + 4^2)`
`=sqrt(9 + 16)`
`=sqrt(25)`
`=5`
2. Calculate the direction cosines of vector `vec A`
`cos alpha=(A_1)/(|vec A|)=3/5=0.6`
`cos beta=(A_2)/(|vec A|)=4/5=0.8`
This material is intended as a summary. Use your textbook for detail explanation.
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