find Parametric equatŁions Far the lihes 1 The line through (L11) Parallel tathe Z gris 2-The like through (2.4,5) perechdicylar to the -52=2t plane 3x+74 3 The lihe throughto,to) Perfendicular to 4hघ १\५Ae the plahe X+2y+22-13

Q: quation of the hyperb

A: Given,      z=-16

Q: Let T be the plane -3y-z --4. Find the shortest distance d from the point Po-(-5, 4, -2) to T, and…

A:

Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 13. a. Distance between parallel planes Show that the dis- tance between the parallel planes Ax + By…

A:

Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: 2 Wnte down the paranuetric equatun of the line l = a nB of intersection of the plane af given by…

A: Given planes are                                                         α:x+2y-3z=0β:2x-y+3z=4 we…

Q: 7. (a) Find the angle between the line == and the plane 2x + y+ 2z + 5 = 0. (b) Test the lines =4 =…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: (42) is the distance between the point (1, –3, –2) and the plane x- 4y-3z-2= 0.

A: In this question we have to find the distance between point and plane. Note: As per our policy we…

Q: CAn equation of the plane through the point (2, 5, 7) that is parallel to the line 7 (t) = 3î + 2ĵ -…

A: Given problem:-  Find an equation of the plane through the point (2, 5, 7) that is parallel to the…

Q: Among all the points on the graph of z = 11-x² - y? that lie above the plane x+ 5y + 6z = 0, find…

A:

Q: A Find equationaf the plane which inderssectnthe line (x-6aut y=-7+34 2--1) atx =2Parallelta the…

A:

Q: Find equations for the planes. Knowing that the plane through the point PO (0, 2, -1) normal to.…

A:

Q: equantion for the tongent plane to the quadratic Z =4x² +y" at the point (4,4,5). Find an surface

A: we have to find the equation for the tangent plane

Q: -) Find the distance between the point and the plane. (0, 0,0) a. + Z = 28 4x +7y+z = 28 b. Verify…

A:

Q: Let T be the plane 3x-3y+2z =4. Find the shortest distance d from the point Po-(-5, 1, 4) to T, and…

A: Given 3x-3y+2z=4and P0=-5,1,4

Q: Find the plane determined by the intersecting lines. y = 2+2t y = 1+ 2s z= 1- 4t L1 x= - 1+t L2 x=1-…

A:

Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: Q3: If P, Q and R are three points having coordinates (3, -2, -1), (1, 3, 4), (2, 1, -2) in XYZ…

A: Given that P(3,-2,-1); Q(1,3,4); R(2,1,-2) are three points in XYZ space.we need to find the…

Q: 4. Consider the plane : x + 3y - 2z = 6 and the line with parametric equations l: x=4-3t, y=2+t, z =…

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: 3 find +he equation of Hhe plane perpendicul av bo the plane x+24+5z=|| and passing through the…

A: The given plane is,

Q: Calculate the shortest distance between the point P = (3, 2, 2) and the plane 5x+y-2z = 3. (Do not…

A:

Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: The plane containing the point (-7,-1,0) and parallel to the plane 5x + 8y – 2z Ax+By+ Cz = D. If A…

A: Given the plane containing the point (-7,-1,0) and parallel to the plane 5x+8y-2z=-5 has the…

Q: Find the plane determined by the intersecting lines. z =1- 3t z = 2- 2s L1 x= - 1+2t L2 x=1- 4s y =…

A:

Q: 6) Find the distance between the point (1, -4, -3) and the plane 2x – 3y + 6z = - 1.

A:

Q: 4. Calculate the distance between the point Q(3, 1, 7) and the plane 2x-6y-z=3. Don't use a formula.…

A: Given point Q(3,1,7)and the plane 2x-6y-z=3. The objective is to find the distance between the point…

Q: (b) The points (2, 2, +3) are on this quadric surface. Using a distance formula, de- termine which…

A: The answer is given as follows:

Q: 24: a) Find the ditane, bel ween the origin and th line %3D %3D (x -22=3 b) Find te intersection…

A:

Q: Q1/: Find the distance between plane (6x - 2y - z +4 = 0) and point (3, 2, 1). (6 marks)

A:

Q: 8) Find the parametricequation of the Line passes through p(2, 13to 3x+y-22 =5 and perpendicularof…

A:

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z=12

A: As there are multiple questions, the first one (19) is solved here.

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

A:

Q: Q.2C) In the xyz-plane determine the distance and angle from point (2,1,1) in the space and two…

A: We have to solve given problems:

Q: Find the intersection of the two planes with equations 3(x – 1) + 2y + (z + 1) = 0 and (x – 1) + 8y…

A:

Q: lo. find a point in the plane x+2y+3z=13 nearest to the point (1,1) usung the methed of Lagrange's…

A:

Q: 3. True or false: a. Collinearity implies coplanarity. b. Any three points are coplanar. c. Any…

A:

Q: Find the eguation f Plane that Passes through P(12-1,3) and s Parallel to the Plane 3X++6? ans. 3X+y…

A:

Q: Find the plane determined by the intersecting lines. y = 2+t L1 x= - 1+t z= 1- 2t L2 x= 1-4s y = 1+…

A:

Q: Find the plane determined by the intersecting lines. y = 2 + 2t L1 x= - 1+ 3t Z = 1- 4t L2 x = 1- 4s…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Q = (-1,3,–1) on the plane Find the point P nearest to x – 4z = 2

A: Given, Q=(-1,3,-1) x-4z=2 (equation of plane) x-4z-2=0

Q: 13. a. Distance between parallel planes Show that the dis- tance between the parallel planes Ax + By…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find. the. parametri.. a. the. line. passes thrayh. (1,2,-1)-l,a1 b.. the.line.passes throuh.(3.p-2,…

A:

Q: Find the Point P of intersection the line X-22-3=o,y-2t=o with the plane X+3y-Z+4=0 and the distance…

A:

Q: 5. Cakculate the distance between the point (3. 1. -2) and the plane 2x + y - z+1-0 O 10 /14 O -10…

A: Find the distance between point and plane?  Value of k for det A= -4