Find the shortest distance from the point P(2,3,0) to the plane 5x +y + z =1 and the corrdinates of the point Q on the plane that is closest to the point P(2,3,0)
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Find the shortest distance from the point P(2,3,0) to the plane 5x +y + z =1...
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
Use Lagrange multipliers to find the shortest distance from the point (2,0, -9) to the plane x + y + z = 1 MY NOTES ASK YOUR TEACHER 10. DETAILS SESSCALC2 11.6.049. Find parametric equations for the tangent line to the curve of Intersection of the paraboloid = x2 + y2 and the ellipsoid 3x +212 +722 - 33 at the point (-1,1,2). (Enter
5. (a) Show that the point Q(1,0,0) lies in the plane x + y + z = 1 and the point P(1, -2,4) does not. (b) Find both the scalar and vector projections of the vector PQ onto the vector a = (1,1,1). (c) Use the scalar projection in (b) to find the distance from the point P(1, -2, 4) to the plane x+y+z=1.
Please solve using the distance formula, not Lagrange multipliers. 5. (11 points) Find the shortest distance from the point P (0, 4,1) to the cone z = Vx2y2 5. (11 points) Find the shortest distance from the point P (0, 4,1) to the cone z = Vx2y2
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%) Find a plane tangent to S at the point P(1, 1, 2) (b) (5%) Find the direction where the derivative of S at P is the steepest (largest) (c) (5%) Find the unit shortest line one S that passes P () (d) (15 %) Determine the flux of F xi+ yj+ zk out of S. s (x, y) y X 1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%)...
du Evaluate dy at (x,y,z)= (2,3,0) for the function (0.0,5) = < Pa cos (); p=51, q=x? Iny,r=z. OA. O OB. 2 3 O c. 6 O D. 18 Click to select your answer.
Q2. Consider the plane P C R3 given by the equation 2z-y+2z 7 and the point v2 (a) Show that the point p-5lies in P and calculate the distance between p and v (b) Find the point qE P that lies closest to v (c) What is the distance of v to P? (d) What is the angle between the vectors v - q and p -q? (e) Does the pythagoras theorem apply to the triangle formed by the points...
3. Find the shortest distance from the center of the quadratic surface 9 x2+54 x +4 y-4 y + 36 z+ 108 z + 73 = 0 to the line of intersection of the planes x + y-z = 10 and -x + 4 y + 8 z = 50 (i.e. Find the shortest distance from the point to the orange line below) 3. Find the shortest distance from the center of the quadratic surface 9 x2+54 x +4 y-4...
(3) On page 136 of the workbook, we developed a formula for the shortest distance from a point to a plane. To briefly recap, suppose P = (21,41, 21) is a point with corresponding position vector p, and II is a plane with normal n = (a, b, c) given by ax + by + cz = d. Then the shortest distance from P to the plane is given by p-q|l, where Q is the point (with corresponding position vector...