Find the point on the plane 5x+3y+: =11 that is nearest the origin. What are the values of x, y, and : for the point ?

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

A:

Q: Q2: Find the equation of the plane that pass through the point P(-1,4,2) and containing the line of…

A:

Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

Q: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

A:

Q: d. Find the equations of the two parallel planes that are distance 5 away from plane P.

A:

Q: Find the distance from the point to the given plane. (-7, 9, 2), x – 2y – 4z = 8 Need Help? Read It

A:

Q: XZWY is a rhombus with diagonals XW and ZY intersecting at point M. Given YMX = 3p + 6, solve for…

A: diagonals of rhombus makes right angle at ntersection point

Q: Find the equation of the plane through the point P= (3,3,5) and parallel to the plane y – 5x + 5z =…

A:

Q: Find the equation for the plane through Po(7.- 3. - 1) perpendicular to the following line. x=7+t,…

A: Ans     equation  of  line          x=7+t,   y=-3-3t,  z=-2t  or   x-71=y+3-3=z+0-2

Q: On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest…

A: Given planes, y+2z=12andx+y=6 Consider the point of intersection be x,y,z.

Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: 23. The distance of the origin from the plane 2x – 3y + 6z = 14 is A 2 В 14 C с -2 D -14

A: on solving that we get

Q: Find the equation for the plane through Po(4,9,8) perpendicular to the following li x= 4+t, y = 9+…

A: Given x=4+t  , -∞<t<∞y=9+2tz=-5tx=t=x-41 , y=t=y-a2  , z=t=-z5

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 – t, z = 3 + 2t. Write…

A:

Q: @/ Find the angle between the planes (x-+y+z=1)and (x-2y+32-1). And find the symmetric equations for…

A: Given equations of planes are x+y+z=1 and x-2y+3z=1 Here, a1=1,b1=1,c1=1 & a2=1,b2=-2,c2=3…

Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

A:

Q: Find the distance between the parallel planes 2x +y + z = 0 and - 6x – 3y-3z – 13 = 0. | NOTE: Enter…

A:

Q: Find the equation for the plane through the points Po (0, – 4, – 5), Qo(4,2,3), and Ro (0,3, – 2).

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 22 — 0. - NOTE:…

A: Find the distance between the parallel planes.

Q: Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

Q: Q1 What is the distance between the point (2,8, 5) and the plane r- 2y-2z = 1 ? a) 5 b) 25 c) 9 d) {…

A:

Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

A:

Q: Find the equation for the plane through Po(6, – 3,7) perpendicular to the following line. x= 6+t, y…

A: Given equation of the lines are, x=6+t, y=-3-5t, z=5t The given equation of the lines can be written…

Q: Find an equation for the plane that contains the line x = − 1 + 3t, y = 5 + 3t, z = 2 + t and is…

A: We need to determine the equation of the plane that contains the line: x=-1+3t, y=5+3t, z=2+t and is…

Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

Q: The equation of the plane which is parallel to y -axis and cuts off intercepts of length 2 and 3…

A:

Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

A:

Q: U and R are the midpoints of the legs, PT and QS, of trapezoid PQST. If PQ = -z + 70, RU = -z + 83,…

A: The solution is given below:

Q: Find the equation for the plane through Po(4,9,-7) perpendicular to the following line. x-4+t,…

A:

Q: Draw the plane given by the equation. x + y + z = 4

A: x+ y+ z= 4

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

A:

Q: Find the distance, d, between the point S(5,6,5) and the plane 6x + 7y + 1z = 12. The distance, d,…

A: topic- distance between point and plane shortest distance of plane ax+by+cz+d from point…

Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x…

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is…

Q: Find the distance between the point P(1, -2, -3) and the plane x + 2y + 2z - 15 = 0. Answer:

A:

Q: Q/ Find the angle between the planes (x+y+Z=1)and (x-2y+32=1). And find the Symmetric equations for…

A: We have to find angle between two planes

Q: Find the intersection of the line and plane: x + 3y – 4z = 18, r(t) = (-3, 2, –2) + t(-3, 2, – 1)…

A:

Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

A:

Q: For the plane, 6x + 10y + 15z = 30, the values of the x-, y-, and z-intercepts are %3D 5, 3 and 2 3,…

A:

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

Q: Q3/ The distance between the plane 2x+4y-4z-22%-0 and the point(1,-2.2) will be ?

A: Basic 3d geometry problem

Q: Find the distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

A:

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2). O…

A:

Q: Find the coordinates of all points (x, y) that lie on the line whose equation is 2x + y = 8, so that…

A: Given: The coordinates of all points x,y that lie on the line whose equation is 2x+y=8, so that the…

Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

A:

Q: Find the angle, in degrees, between the 2 planes with equations X-y+3z=1 and 3x+ y-z=D2

A: Take the normal vectors of the planes x-y+3z-1=0 and 3x+y-z-2=0 as N1⇀ and N2⇀ respectively.…

Q: Find the distance between the parallel planes P and P P: 2z -y+ 3z -6 =0 P: 4z - 2y + 6z - 2 =0

A: Distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is…

Q: Find the point on the plane 2x + 5y + z =9 that is nearest to (2,0,1). Vhat are the values of x, y,…

A:

Q: Find the distance, d, between the point S(9,3,5) and the plane 9x + 1y + 1z= 36. The distance, d,…

A: