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graydarl
 3 years ago
I have A(1,2,1), B(1,2,3), C(2,2,2)
pi: x2*y+2*z = 0
d: (x1)/2 = y/(1) = (z1)/(2)
And i need to find:
 area of ABC
the equation of the plane ABC
distance from point A to plane pi
distance from A to the line d
equation of perpendicular line from A to the plane ABC
graydarl
 3 years ago
I have A(1,2,1), B(1,2,3), C(2,2,2) pi: x2*y+2*z = 0 d: (x1)/2 = y/(1) = (z1)/(2) And i need to find:  area of ABC the equation of the plane ABC distance from point A to plane pi distance from A to the line d equation of perpendicular line from A to the plane ABC

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Hoa
 3 years ago
Best ResponseYou've already chosen the best response.1calculate for vector AB = <0, 4,4> calculate for vector BC = <1,4 1> calculate vector AB cross BC = <12,4,4> the area of ABC = 1/2 sqr ((12)^2 +4^2+$^2) = 2 sqr(11)

Hoa
 3 years ago
Best ResponseYou've already chosen the best response.1the last sentence means areaABC = 1/2 the product of AB cross BC

Hoa
 3 years ago
Best ResponseYou've already chosen the best response.1to get the equation of plane ABC you need the normal vector n of the plane which is orthogonal with the plane. It is AB cross BC . As previous part we have, vector n = <12,4,4> . so a = 12, b= 4, c = 4 then apply to formula for equation of the plane . I choose the point A(1,2,1) to apply. that is a(x1) + b (y2) +c(z+1)=0 . At the end up, the equation is: _12(x1) +4(y2) +4 (z1)=0 or you can expand it to get more simple form.

graydarl
 3 years ago
Best ResponseYou've already chosen the best response.0i did not understood this part: then apply to formula for equation of the plane . I choose the point A(1,2,1) to apply. that is a(x1) + b (y2) +c(z+1)=0 . At the end up, the equation is: _12(x1) +4(y2) +4 (z1)=0 or you can expand it to get more simple form.

graydarl
 3 years ago
Best ResponseYou've already chosen the best response.0another thing, by : "the last sentence means areaABC = 1/2 the product of AB cross BC" you mean that the line l for example will have the coordinates (6,2,2) ?

Hoa
 3 years ago
Best ResponseYou've already chosen the best response.11st question: that means based on the point you choose to apply the formula, you have a distinguished equation for the plane. I choose the point A to apply the formula. you can choose B or C. we have so many equations for one plane. from my equation, I expand to 12x +12 +4y 8 +4z 4 = 0 . then simplify it to 12x + 4y + 4z = 0 2nd question: that the theorem from the lecture. review it from page 811 example 4 of the book calculus by James Stewart. Hope this help
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