In Exercises 1-8, write the equation of the plane with normal vector n passing through the given point in the scalar form ax+by+cz = d. n =(-1,2,1), (3,1,9)

Write the Equation of a Plane in Vector form and Scalar form.

In R3, derive the equation of a line in vectorial, parametric and canonical form.

Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1, 1) in the scalar form ax + by + cz = d.

Determine the vector and cartesian equation of the plane that passes through the pointsA(−3, −2,0), B(1,3, −1) and C(−1,2,4)

Find the equation of the plane in xyz-space through the point P=(2,5,5) and perpendicular to the vector n=(1,−4,−5).

Write the equation of the plane with normal vector n = (-6, 4, 2) passing through the point (4, 6, 5) in scalar form ax + by + cz = d. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:

Use linear algebra to find the vector equation of the line of intersection of the planes, 3x₁2x₂ + x3 = 4 and x₁ + 2x3 = 2.

Find an equation of the plane through the three points P =(0,0,4), Q=(-3,4,0), R=(-1,-2,3). You can write your equation in general form or scalar form.

Determine the scalar, vector and parametric equations of the plane that passes through thepoints (3,2,5), (0,-2,2) and (1,3,1). find each individual equation.