(5.1) Find the vector form of the equation of the plane that passes through the point P0 = (1, −2, 3) and has normal vector ~n =< 3, 1, −1 >.

Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) + s(4,-5,1). Please answer  Thank you.

Let / denote the line in R² with equation y = 3x - 2. Let Q = (2, -1). (a) Write the line / in vector form (i.e. of the form p = po + td where Po is a point on the line and d is a direction vector). (b) Find the distance from Q to 1. (c) Find the point on I closest to Q.

Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and perpendicular to the plane 4x-y+2z=7?

Determine the equation of the tangent plane and a vector equation of the normal line to x²y - 4ze+y +35= 0 at (3,-3,2). A. tangent plane: -26x + y −4z +89 = 0, normal line: (3+26t, -3-t, 2+4t) B. tangent plane: -26x + y - 4z +89 = 0, normal line: (3-26t, -3+t, 2-4t) C. tangent plane: 26x + y − 4z +89 = 0, normal line: (3+26t, -3-t, 2+4t) D. tangent plane: 26x + y - 4z +89 = 0, normal line: (3-26t, -3+t, 2-4t)

First find the equation of a plane through the point (4, 2, 1) with normal vector = 3ī − 2j + 4k. Next find the equation of the line through this same point (4, 2, 1) and with direction parallel to this normal vector i = 3ī −2j+ 4k. (this line is called the normal line to the plane) Now graph both this plane and the normal line together. 10 ستید 10 تند مسك

Find an equation of the plane that passes through the point Po(0, -2,3) with a normal vector n = (1,-1, 1). The equation of the plane that passes through the point Po(0, -2,3) with a normal vector n = (1, -1, 1) is (Type an equation.)