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aa1604962
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Find the intersection.
x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10
x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10
MHB Where Do These Parametric Equations and Plane Intersect?
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To find the intersection of the parametric equations and the plane, substitute x, y, and z from the equations into the plane equation -2x + 8y + 8z = 10. This leads to the equation -2(-5 + 8t) + 8(1 + 10t) + 8(9 + 8t) = 10. Simplifying this will yield a value for t, which can then be used to find the corresponding x, y, and z coordinates. The intersection point can be determined by solving for t and substituting back into the parametric equations. This process effectively identifies where the parametric line intersects the defined plane.
Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...
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