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Determine if the point (4,-2,3) lies in the plane with vector equation (x, y, z) = (2,...

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oyechalphut | Student, Grade 10 | (Level 1) Honors

Posted March 11, 2013 at 6:26 AM via web

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  1. Determine if the point (4,-2,3) lies in the plane with vector equation (x, y, z) = (2, 0, -1) + s(4, -2, 1) + t(-3, -1, 2).

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mathsworkmusic | (Level 1) Educator

Posted March 11, 2013 at 2:44 PM (Answer #1)

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Let (x,y,z) = (4,-2,3). Rearrange the set of three equations to give

1) 4s - 3t + 2 = 4 implies 4s - 3t = 2

2) -2s - t + 0 = -2  implies -2s - t = -2

3) s + 2t -1 = 3 implies s + 2t = 4

 

Add 1) and 2) together giving

2s - 4t = 0  implies  s = 2t

Putting this in to 3) and solving gives t = 1 (and hence s = 2)

Check this against equation 1). 4(2) - 3(1) = 5

This does not give the correct result, therefore the point (4,-2,3) does not lie on the plane defined by the vector equation.

 

 

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