Write an equation of the plane with normal vector n =⟨−7,−4,−6⟩ passing through the point (−8,4,6) in scalar form in the form of equation = 20

Consider the line ` in R^2 with normal vector n = [1, −5] and passing through the pointP = (−3, 4).(a) Write down equations in normal form and general form for this line.(b) Use the general form to find parametric equations for `, and then write down avector equation for ` as well.(c) Hence or otherwise write down a direction vector for `.ChatGPT

Find a normal vector n𝑛 to the tangent plane to the surfacez=−3x2y3𝑧=−3𝑥2𝑦3 at the point (x,y,z)=(−3,4,−1728)(𝑥,𝑦,𝑧)=(−3,4,−1728) and enter your answer in the box below using Maple syntax.  n=𝑛=

Consider the function F (x, y, z) = 2x5 + 3x2y − 2xz + y6 + z2 − 6.(a) Find a vector point-normal and scalar equation and a vector parametric form for thetangent plane to the surface F (x, y, z) = 0 at the point p = (−1, 0, 2).

Find an equation of the plane. the plane that passes through the point (3, 6, −1) and contains the line x = 4 − t, y = 2t − 1, z = −3t

Which of the following is a plane passing through the points [1,1,−2][1,1,−2], [3,4,−3][3,4,−3], and [−2,−1,8][−2,−1,8]?Please select all correct answers.[1,1,−2]+s[2,3,−1]+t[−3,−2,10][1,1,−2]+𝑠[2,3,−1]+𝑡[−3,−2,10][1,1,−2]+s[2,3,−1]+t[−5,−5,11][1,1,−2]+𝑠[2,3,−1]+𝑡[−5,−5,11][1,1,−2]+s[3,4,−3]+t[−5,−5,11][1,1,−2]+𝑠[3,4,−3]+𝑡[−5,−5,11][1,1,−2]+s[3,4,−3]+t[−2,−1,8]