Write the scalar equation of this plane. [x, y, z] = [5, 4, -7] +s[0, 1, 0] +t[0, 0, 1]

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Write the scalar equation of this plane. [x, y, z] = [5, 4, -7] +s[0, 1, 0] +t[0, 0, 1]

Mathematics
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i know i have to find the direction vectors
  • phi
I think [0 1 0] and [0 0 1] are orthogonal to the vector normal to the plane if you from the cross product, you get [1 0 0]= N (the normal vector) N dot [x y z] = constant is (almost) in the form of a scalar equation (a x + b y +c z= d) N dot with any point on the plane (5 4 -7 is a good choice) gives the constant: N dot [5 4 7]= 5 so that is the equation: [1 0 0] dot [x y z] =5 that simplifies to x = 5 as the scalar form
Thank youuu !!!

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