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  (a) Determine the point of intersection of the line given by (x, y, z) =...

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Basic Math

 

(a) Determine the point of intersection of the line given by (x, y, z) = (4+t, −1+8t, 3+2t), t ∈ R with the plane given by 2x − y + 3z = 15 or show that they do not intersect.

(b) Given the line L : X = (9, 13, −3) + t(1, 4, −2), t ∈ R, the point A with position vector 4i+ 16j −3k and that the point P lies on L such that AP is perpendicular to L, find the exact coordinates of P.

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