axby3z- k passes through (5,1,1) and (4,0, -2) Given that plane 2y 3z It is also...
Q4. (5 points). Find the equation of the plane that passes through the line of intersection of the two planes x - 2y = 3 and y- z = 0 and parallel to the line x = y - 1 = 2+1 Q5. (4 points). Find the distance from the point A(1,2,3) and the line 2+1 y-1 2 Q6. (4 points). Give the name and sketch the surface whose equation is given by x2 + 2y2 – 12y – z...
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 2
Find the normal form of the equation of the plane that passes through Find the vector form of the equation of the line in ℝ2 that passes through P = (5, −2) and is parallel to the line with general equation 5x − 4y = 2.
Does the plane x + 2y – 3z – 4 = 0 meet the line segment from (1,2,3) to (6,5, 3)? Say yes or no and why.
Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 3, 5)
Line JK passes through points J(-3,11) and K(1, -3) O 7x + 2y =-1 (g) 7x+2y = 1 O 14x+4y =-1 O 14x+4y = 1
Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (2,0, 6), and (-3, -1, 9). Find the distance between the point and the plane. (0, 0, 0) 3x + 7y + z = 21 The position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t), of the object. r(t) = ti + Rj+ K
16. [3 points]Write the equation of the plane that passes through the point (0, 2, -1) and contains the line given by x = 2y = 2-3 slo bus dt of boilqqa od ot batin pt 911 di 10 abusingsmorit ei tedatnioq El.AI Cmos lo uprot soubora od 2€ lo algne as te donarw 11-1
Use lagrange multipliers to find the point on the plane x-2y 3z-14=0 that is closet to the origin?(try and minimize the square of the distance of a point (x,y,z) to the origin subject to the constraint that is on the plane) Help me please!
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...