.) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z = 1-s

Q: Find two di¦erent planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t . Write…

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Q: Find the equation of the plane which passes through O and is parallel to z – (5x + 6y) = 3 x+ y + z…

A: see 2nd step.

Q: Let P(x1, y1) and Q(x2, y2) be two points in the plane. Prove that the equation of the line through…

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Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

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

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Q: Find the point at which the line intersects the given plane.

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Q: Show that the lines determined byr 1(t) = <−2 − 5t, 3 + 2t, 4t >andr 2(t) = <8 + 15t, 1 −…

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Q: Determine whether the planes 5x − 3y + z = 4,  x + 4y + 7z = 1 are parallel, orthogonal, or neither.…

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Q: Which of the following is the equation of a plane parallel to the cz-coordinate plane and passing…

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Q: a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1…

A: (a) To show that the distance between two parallel planes Ax+By+Cz=D1 and Ax+By+Cz=D2 is…

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

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: To find the equation of a plane which cuts intercepts a, b, c res- pectively on the axes of…

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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 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: a) Explain fully, atleast three possible relationships between two lines in R3 [c3] b) Which of the…

A: (a) The relationship between any two lines in ℝ3 is always one of the following three: They can be…

Q: Which of the following is the equation of a plane parallel to the yz-coordinate plane and passing…

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Q: Find the eguatien of the tangett line and nemat plane to the cune; Y. cest Ces(zt)i + st sinCet) j +…

A: Given r=cost cos2ti+cost sin2tj+sintk

Q: Which of the following points is on the xz plane? a) (1, -3, 0) b) (0, 4, 0) c) (0, 3, -2) O d) (2,…

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Q: Determine whether the plane x + y + z = 9 and the line x = t, y = -2t + 1, z = t + 2 are parallel,…

A: The given equation of line is in parametric form, x=ty=-2tz=t+2 Convert it into the cartesian form,…

Q: 23. Through (1,3, 5) and normal to7 - } +k.

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

Q: Consider the line which passes through the point P(5, 2, -1), and which is parallel to the line x =…

A: Introduction: In three dimensional geometry, there are three fundamental planes referred to as the…

Q: 4. Determine whether the planes are between them. 2x – 3y + 4z = 5; x+ 6y + 4z = 3 parallel,…

A: This question can be solved using the concept of angle between two planes.

Q: If a = i + 3j j k, b = 2i + 4j j 2k and c = = i + 2j + 4k, find a number λ such that d = a + b + λc…

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Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

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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: 3. Consider the plane TT: 4x + 3y - 2z + 12 = 0. What is the relationship of the plane to each of…

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Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: If a = i+3j – k, b = 2i + 4j – 2k and c = -i + 2j +4k, find a number A such that d = a +b+ Xc is…

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Q: (2t+l, st-5, lot ) f 4z: Given two lines ( 34, 2++3, zt+1) located in Sice the plane ? plane, find

A: The required equation for the plane is calculating by the below method.

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

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Q: P, Q and R Find a plane that contains S and is parallel to the plane that contains the points

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

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A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: Given the following line and plane: 1 1 +t. qE R; Plane: I - y +z = 1 Line: 4 3 Determine whether…

A: We have to check weather the line intersects the plane. If they doesn't intersect then we need to…

Q: Which of the following represents a plane surfac whose x-, y-, and z-intercepts are a, b, and c…

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Q: tor that is norma to the Plane determined by the three Points i+ 2j +k, si-j+ k , 3i + 2; - 7k.

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Q: Consider the plane P with equation −2x−2y+z = 1 and line L with equations x = 2−3t y = 9−6t z = −4…

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Q: Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar +…

A: Here we use the distance formula between two points.

Q: Find the intersection of the following geometric objects: the plane 3x - y + z = 3 and the plane 2x…

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Q: What is the equation of a plane whose r-intercept is a, y-intercept is b, and z-intercept is c?…

A: Solve for the equation

Q: Given that A and B are parallel to the yz plane, that |A| = 2, |B| = 4, and A • B = 0, what can you…

A: Consider the provided question, Given A and B are parallel to the yz plane.

Q: Consider the plane P with equation x+2y+2z=-7 and line L with equations x=-4-2t y=4+7t z=-1+3t…

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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: x + 4y + 2z = 4, and 4x -3y +4z = 7.

A: Topic - plane and vectors

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

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