QUESTION 1 For the parametric line L: x = 4+t, y = 3+t, z= 3-2t and the plane P: -y= x+ z + 2, then the line and plane are : O Perpendicular O Neither O Parallel

Q: Question 1: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A)…

A: Given that L is the line of intersection of the planes 2x-y-3z=4 and 2x+y-z=2

Q: Question 22 Consider the plane n :r-z=1 and the line 2 Find the equation of the plane that cantains…

A: Explained below

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

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Q: Part A Find the parametric equations of the line of intersection of the following planes: T1: 5x +…

A: Find the point of parametric equation of the line of intersection, and angle between two planes

Q: 14. State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Two planes are given by, π1: x-y+z-2 = 0  and π2: 2x+y+z-4 = 0. The objective is to check whether…

Q: find the parametric equations of the line through (-3,0,2) that is parallel to 3i-4j+k. x(t)= y(t)=…

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Q: The lines L1 and L2 are determined by the following symmetric and parametric equations,…

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Q: Problem 1. Let L be the line (2t, t, t — 1), t ≤ R, and A the point (1,1,-1). Let P be the plane…

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Q: The parametric equations for a line L7 are as follows: x=-3-2t y 3+2t z = 1-6t Let L, be the line…

A: Find the point P.

Q: Consider two straight lines described by the following parametric equations x = 3+t, y = 4 + 3t, z =…

A: The angle between two vectors  v1 and v2  is,…

Q: Question 6 Let ū = (0, 1, –1), ū = (2, 1, 0) and w = (4, 1, 1). a) Show that ū, ū and ū lie in the…

A: As per the company guidelines we are supposed to solve first 3 subparts of a question untill…

Q: . Consider the plane P : x +y + z = 2 and point A(0,1, 2). A line L has the parametric equations L:…

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Q: QUESTION 5 Let A(-1, 3, 3), B(4, – 1, 0), C(5, 4, –7), and D(2. -1, –1). Find i. the normal vector…

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Q: The parametric equation of the line through the origin that is parallel to the line given by x = t,…

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Q: Consider the lines L and L2 whose symmetric equations are x – 1 L1: y + 1 z + 1 y – 3 z + 4 L2 : 4 –…

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Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Let's solve.

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

Q: Problem 1. Let L be the line (2t, t, t — 1), t € R, and A the point (1, 1,-1). Let P be the plane…

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Q: Q1) Write the parametric equations of the line of intersection of the planes 2x-y+z 5 Note: Consider…

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Q: Consider two non-parallel lines L1 and L2 in R2 with the following parametric equations: (3,6) +…

A: Given : L1 = (3, 6) + s(3, -4) and                   L2 = (-4, -6) + t(2, -4)

Q: (a) Show that the parametric equations x = X1 + (X2 - X1)t, y = y1 + (y2 – Y1)t where 0 sts1,…

A: Given Points are P1(x1,y1) and P2(x2,y2)

Q: Find the point P of intersection between the line x(t) = (-3,-2, 1) + t (1, 1, -3) and the plane 4z…

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Q: Question 5, Find points of intersection of the plane 3x + 4u - 7- 24 = 0 with the axes.

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Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

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

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: QUESTION 1 For the parametric line L: x =4+t, y y =3+t, z=D3+2t and the plane P: -y = x+ 2z + 2,…

A: Compute the direction ratios of both the line and the normal of plane.

Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Given: The equation of two planes are: V1 : x − y + z − 2 = 0, V2 : 2x + y + z − 4 = 0

Q: (s) (a) Find a parametric equation for the line through (2, 4, 6) that is perpendic- ular to the…

A: Equation of line in 3D

Q: Consider the following 2 planes: ?1: 2? − ? − 4? − 4 = 0                   ?2: 4? − 2? − 3? = 3…

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Q: The parametric equations r = 3 - t, y = 2t + 4, 0 <t < 2 describes motion along a certain line…

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Q: Given the following set of parametric equations, find all points of horizontal and vertical…

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Q: Find the parametric equations for the line of intersection of the planes x+y-z = -20 and 9.x + 3y +…

A: Given planes, x+y-z=-20 and 9x+3y+z=16. The objective is to find the parametric equations for the…

Q: Question 13 Which of the following is an equation of a plane surface? O 222 + 3y + 4z = 4 O 2z2 +…

A: Equation of pane surface. Will be of the form ax+by+cz =d

Q: 6) Consider the plane P: z+y-2:= 0 in R³ that contains the point P₁(1, 1, 1). Answer the following…

A: As per the question we are given the plane P and a point P1 on it. Now we have to find the…

Q: Find the projection of v = -7 onto the -2 e of R' given by the parametric equation e = tu, [-11

A: Introduction: The formula of projection of the vector v onto the vector u is given by the formula,…

Q: QUESTION 2 The relation between the two parametric equations of the lines 20 274 t, y=1+6t, L1:…

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Q: QUESTION 2 What is the best descriptor of the object in three-dimensional space given by the…

A: Solution :-

Q: Question 10 Find equations for the planes: a) Passes through P(1,–1,–3) parallel to the plane 3x + y…

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Q: QUESTION 2 (a) Find parametric equation of the line segment ( L ) between the points P(1, 8, 9) and…

A: We will first test for parallels then for intersection

Q: Given points P (4, -2, 5), Q (3, 5, 5), and R (0, 2, 6) find the parametric equation of the line PQ…

A: Here given point  P (4, -2, 5), Q (3, 5, 5), and R (0, 2, 6) So  PQ=2-4, 5--2, 5-5=-1, 7, 0 PR=0-4,…

Q: Question 4 A parametric equations for the circle x² +y² + 4x – 12y = 60 are O A.x =6 + 10 cost, O…

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Q: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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Q: 13. Given the points A(3,5) and B( – 3, – 7), find b. the parametric equations of the line.

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Q: 4. ( Consider points P(1,0, 1), Q(-2,1,3), and R(4,2,5). (a) Find the parametric equations of the…

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Q: Complete the parametric equations of the line through the point (8,6,-2) and perpendicular to the…

A: equation of line passing passing through the point 8,6,-2 and perpendicular to the plane , x-7y-z=-3

Q: QUESTION 2 Plot the surfaces given by: y = Vx? +z? .2 x² + y? - 3+ z? =0 X = 0 in one 3D-space.…

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Q: Question 2 (a) Let S1 be the plane which contain lines L, and L2 whose parametric equations are…

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Q: Please help with the following math question: Give a vector parametric equation for the line…

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Q: QUESTION 2 What is the best descriptor of the object in three-dimensional space given by the…

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