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If the plane cuts coordinate axis at A(2,0,0) B(0,3,0) and C(0,0,6) then find the area of the triangle ABC???

If the plane cuts coordinate axis at A(2,0,0) B(0,3,0) and C(0,0,6) then find the area of the triangle ABC???

Grade:12

1 Answers

Vikas TU
14149 Points
5 years ago
Right off the bat we need to discover AB and AC. 
Abdominal muscle = B – A = (0,3,0) - (2,0,0) = (- 2,3,0) 
Air conditioning = C – A = (0,0,6) - (2,0,0) = (- 2,0,6) 
Presently, we realize that the territory of the triangle ABC is half of the range of the parallelogram shaped by AB and AC and furthermore we realize that the region of that parallelogram is figured as: AB × AC , so registering that cross item we have: 
Abdominal muscle x AC = (18 )i –(- 12)j + 6k 
18i+12j+6k 
Extent is ((18^2 + 12^2 + 6^2)^1/2)/2 
=> ((324 + 144 + 36)^1/2 )/2 
=> (504)^1/2/2 

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