1. Example-1
1. Find AreaParallelogram(A,B)
`A=(1,2,3)`,`B=(4,5,6)`
Solution:
Here `vec A=(1,2,3),vec B=(4,5,6)`
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],[1,2,3],[4,5,6]|`
`=i(2xx6-3xx5)-j(1xx6-3xx4)+k(1xx5-2xx4)`
`=i(12-15)-j(6-12)+k(5-8)`
`=-3i+6j-3k`
`=(-3,6,-3)`
2. Calculate magnitude
`|vec vec A xx vec B|`
`=sqrt((-3)^2 + 6^2 + (-3)^2)`
`=sqrt(9 + 36 + 9)`
`=sqrt(54)`
`=7.3485`
3. Calculate triangle area
Area `= 7.3485`
2. Find AreaParallelogram(A,B)
`A=(5,-1,1)`,`B=(-2,3,4)`
Solution:
Here `vec A=(5,-1,1),vec B=(-2,3,4),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,-1,1],[-2,3,4]|`
`=i((-1)xx4-1xx3)-j(5xx4-1xx(-2))+k(5xx3-(-1)xx(-2))`
`=i(-4-3)-j(20+2)+k(15-2)`
`=-7i-22j+13k`
`=(-7,-22,13)`
2. Calculate magnitude
`|vec vec A xx vec B|`
`=sqrt((-7)^2 + (-22)^2 + 13^2)`
`=sqrt(49 + 484 + 169)`
`=sqrt(702)`
`=26.4953`
3. Calculate triangle area
Area `= 26.4953`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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