2. Example-2
1. Find AreaParallelogram(A,B)
`A=(5,6,1)`,`B=(0,2,3)`
Solution:
Here `vec A=(5,6,1),vec B=(0,2,3),vec C=(3,4,5)`
Area `=|vec A xx vec B|`
1. Calculate cross product
`vec A xx vec B`
`=|[i,j,k],[A_1,A_2,A_3],[B_1,B_2,B_3]|`
`=|[i,j,k],[5,6,1],[0,2,3]|`
`=i(6xx3-1xx2)-j(5xx3-1xx0)+k(5xx2-6xx0)`
`=i(18-2)-j(15-0)+k(10-0)`
`=16i-15j+10k`
`=(16,-15,10)`
2. Calculate magnitude
`|vec vec A xx vec B|`
`=sqrt(16^2 + (-15)^2 + 10^2)`
`=sqrt(256 + 225 + 100)`
`=sqrt(581)`
`=24.1039`
3. Calculate triangle area
Area `= 24.1039`
2. Find AREAPARALLELOGRAM(B,C)
`A=(5,6,1)`,`B=(0,2,3)`,`C=(3,4,5)`
Solution:
Here `vec A=(5,6,1),vec B=(0,2,3),vec C=(3,4,5)`
Area `=|vec B xx vec C|`
1. Calculate cross product
`vec B xx vec C`
`=|[i,j,k],[B_1,B_2,B_3],[C_1,C_2,C_3]|`
`=|[i,j,k],[0,2,3],[3,4,5]|`
`=i(2xx5-3xx4)-j(0xx5-3xx3)+k(0xx4-2xx3)`
`=i(10-12)-j(0-9)+k(0-6)`
`=-2i+9j-6k`
`=(-2,9,-6)`
2. Calculate magnitude
`|vec vec B xx vec C|`
`=sqrt((-2)^2 + 9^2 + (-6)^2)`
`=sqrt(4 + 81 + 36)`
`=sqrt(121)`
`=11`
3. Calculate triangle area
Area `= 11`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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