3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 - 4s, -00

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: 2. Find the equation of the plane containing the lines L1: (x-2)/2 = (y+1)/-1 = z/3; L2: (x+1)/2 =…

A: Given that:L1: x-22=y+1-1=z3L2: x+12=y-1=z+23

Q: 5. Determine the equation of the plane that contains the point (0,3,0) and the X = 1 line y = 2t z =…

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Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

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Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: Sketch the plane curve. r(t) = 4ti – tj, [0, 4] %3! y y 4 4 2 X 10 15 10 15 -2 -2 y y 4 4 2 10 15 10…

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Q: Let P be the plane that is tangent to the equation xyz + 260 = z' + 30x + 26y at the point (7,7,4)…

A: The tangent plane to the surface is a plane that only touch the surface at the point.

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: At what point does the line :LiX==€ 1=10+8€ 14. -2y t52 +16:0 10+3€ z=41+3€ intersect with the plane…

A: Question is based on 3d Geometry.

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: What is the intersection of the plane x+2y+z =0 and the line (x, y,z) = (0,1,2)+ k(–1,1,2), kER?

A: Consider the equation of plane x+2y+z=0 and the equation of line x,y,z=0,1,2+k-1,1,2. Find the…

Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

Q: Determine the way in which the line [x, y, z] = [2,−3, 0] + k[−1,3,−1] intersects the plane[x, y, z]…

A:

Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: Find the point where the given line intersects the given plane x = 1-t, y = t, z = 1+t, z = 1- 2x +y

A: Given lines, x=1-t , y=t  , z=1+t  Given plane, z=1-2x+y To find the point where the given line…

Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: 22 Prove that the line Z=2+46 is perpendicular to thme plane X-2y+2=6

A: As per our guideline we are supposed to do 1 question at a time. Please post other questions next…

Q: Let L be the line x = t, y = -11 - 7t and z = -6 - 3t and let M be the line x = 1 +s, y = 2s and z =…

A:

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

A:

Q: Show that the line x + 1 =y/−1=(z − 2)/2 is in the plane 2x + 4y + z = 0.

A: Given equation of a line, x+1=y-1=z-22 And equation of a plane, 2x+4y+z=0

Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by the…

Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: 25. Determine the distance between the parallel line {y = 5-t, te R and the plane {y = 2-s -t, s,t E…

A:

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y -…

A: We have to find the point at which the line intersects the given plane.

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: Q1. A) Determine if the plane given by -x + 2z = 10 and the line given by %3D (x = 5,y = 2 - t,z =…

A: Consider the given values. -x+2z=10 And, (x=5, y=2-t, z=10+4t)

Q: Find the plane containing the intersecting lines x = -1+t, y = 2+ t, z =1–t; -0 <t < o∞ | L2: x = 1…

A: Find the planes containing the intersecting lines: L1:x=-1+t,y=2+t,z=1-t for all…

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

A:

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

A:

Q: What is the symmetric equation of the line that is normal to the plane x + y + z = 9 at the point…

A:

Q: Show that the condition that the curves ..(1) ..(ii) ax? + by =1 %3D a'x² + b'y² = 1 1 1 1 Should…

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Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line…

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Q: Show that the line through two distinct points (x1, y1) and (x2, y2) in the plane has equation: | x…

A: Solution..

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

Q: find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2

A:

Q: 7 Find the Paametric equ. for the line f intersect of the Planes 3x- 6y -2z =15 and 2X+Y-22%3D5?…

A: Given two lines, 3x-6y-2z=15 ....(i) and 2x+y-2z=5....(ii) Putting z=0 in (i) and (ii) we get,…

Q: Find m, n ∈  R so that the line r X: (n, 2,0) + λ (2, m, m) is contained in a plane π: x -3y + z = 1

A: The direction cosines of the line, r(x)= (n, 2,0) + λ (2, m, m) are &lt;2, m, m&gt; . The direction…

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

A:

Q: Find the plane determined L1: x=-1+t 12: x=1-4s by the intersecting lines: y=2+t y=1+2s 2=1-1-3-1-00…

A:

Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

A:

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: 4. Find the point of intersection of the plane z= 4 and the line L={ (x, y, z) | x= 4 + 3t, y=-1-2t,…

A:

Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

A:

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

A:

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: At what point does the line r(t) = (6- 3t)i + (-2 + 2t)j + (-1- 3t)k intersect the yz-plane %3D O a.…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.