c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

Q: Sketch the plane curve r(t) = 2ti − 3tj,  and find its length over the given interval [0, 5]

A: Given plane curve: The parametric form of vector valued function is It is the equation of line in…

Q: 3-Find the equatium uf tue plone that is parllel and at (& units) Aujay From The plane (x-ay+t=3)

A: The equation of the given plane is  x-2y+z=3

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: The distance from a point S(xo,yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n · PS| d In|…

A: From a point S(x0,y0,z0) to the plane M = ax+by+cz+d=0 Let S1=x1,y1z1 be any point in the given…

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

A:

Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

A:

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

A: Given: The equation of plane 5x+3y+z=11, To determine: The point on the plane that is nearest the…

Q: 4. Find the angle made between the two planes: r+ y - z = 5 and 2r + y +3z = -1.

A: Given that: Equation of first plane: x+y-z=5   ........(1)Equation of 2nd plane: 2x+y+3z=-1…

Q: O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

A:

Q: Find the angle between the plane r+y-z=21 and the line r-13y+2%3D3-2z.

A: Angle between the plane and line

Q: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

Q: Which is the fourth point on plane TSW? T. U O Y

A: A plane is a 2-dimensional surface. It can have an infinite number of points. A plane is composed of…

Q: Find the cosine of the angle between the planes x + y + z = 0 and x + 4y + 3z = 2.

A:

Q: H.W: Find the distance from S (1,1,3) to the plane 3x+ 2y+ 6z = 6

A:

Q: Match the surfaces (a)-(e) with the contour diagrams (1)-(V, (M)

A:

Q: The distance from (4,-5, 10) to yZ-plane is O A.4 O B. 5 C. /141 OD.10 OE. 125

A: Solution is given below:

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

A:

Q: For what positive value of cc is the acute angle between the plane containing the points A(0,0,1),…

A: According to the given information, it is required to find the positive value of c is the acute…

Q: o Find an equahion for the plane throught (l,-l,3) parallel fo the plane 3x ty+Z =7

A:

Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

A:

Q: 1. Consider the planes P and Q given as 2x- 3y +2 = 3 and 4x- 6y + 22 = 5. Are P and Q parallel?…

A:

Q: Find the angle (in degrees) between the planes 4y + z = 4 and – 4x + 2z= - 3.

A:

Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

A:

Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

A:

Q: Which is the fourth point on plane TSW? S T U Y O Y O W

A: we have, As we can see that a cuboid is given and their vertex are assigned by some letters. Always…

Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

A:

Q: Consider the line L(t)=⟨4t−1,2−5t,−3−4t⟩. Is L parallel, perpendicular, or neither to the plane…

A: Lt=<4t-1 , 2-5t , -3-4t >Direction ratio of Lt=< 4 , -5 , -4 >Normal vector to given…

Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

A:

Q: x − 3y + 6z = 4 e 5x + y − z = 4

A: For the equation of plane a1x+b1y+c1z+d1=0, a2x+b2y+c2z+d2=0The angle between them is given…

Q: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

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: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

A:

Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

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

A:

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

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 an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

A:

Q: Find the cosine of the angle, 0 Ses x/2, between the plane x +2y-2z= 2 and the plane 4y-5x + 3z =…

A:

Q: Q2) Find the distance from the point P (1, 2, 3) to the plane x-3y + 2z= 4.

A:

Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n PS| d =…

A:

Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

A:

Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: Let fiz) = x2 + iy? where x and y are the real and imaginary parts, respectively of z and C is a…

A:

Q: Find the distance between the origin and the intersection line of the planes : 2x+y+z=2 and x+2y+z=3…

A:

Q: Find the point of intersection between the planes TT :x+y-z =1, n, : 2x – 3y -9z = 10 and n, : x +…

A: The three planes are, π1=x+y-z=1 π2=2x-3y-9z=10 π3=x+2y-3z=-4

Q: Q2. A. Show that the plane 3x +y- z = 9 and the line {x 2,y =-1+ 3t,z 1+ 3t} are parallel, then find…

A: Answer

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: Calculate the vector normal to the yz plane. Equation of yz plane:x=0Equation of vector normal to yz…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.