Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point  (3, 2.5, 3.1)  and parallel to the vector  2i + 4j − k r(t)  =           (x(t), y(t), z(t))  =

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Proceed as shown below...

Q: (A) Find the parametric equations for the line through the point P = (-4, -3, -5) that is…

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Q: A) Find the parametric equations for the line through the point P = (3.-5, 1) that is perpendicular…

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Q: (a)i Find a vector equation and parametric equations for the line that passes through the point A(5,…

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Q: Give the equation of the line in vector form, parametric form and symmetric form. The line through…

A: Given line is  The direction ratios of given line are proportional to <-3,9,-1>. Since the…

Q: 1. Find parametric equation for the line through the point P(3,-4,-1) parallel to the vector v…

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Q: Find parametric equations for the lines in The line through the point P(3, -4, -1) parallel to the…

A: Given P3,-4,-1r=ro+tvro=3,-4,-1,ro=3i∧-4j∧-k∧v=i∧+j∧+k∧

Q: Exercise 1 The parametric equation of the line through the points (2,-4,1) and (0,4,-10) is: A. x =…

A: exercise 1) given points 2,-4,1 , 0,4,-10 claim- to find the parametric equation of line through the…

Q: 4

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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Q: Find a vector equation and parametric equations for the line that passes through the point (2,1,-3)…

A: We have to find out

Q: 3+z Given the points R (1, -1, -3), the vector v = and the line d: ¯x+¹=1+y= 3 2 3. Calculate the…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given that , Point =0,0,0 and parallel line r=3+2t , 7-6t , 5+4t find vector and parametric equation…

Q: Exercise I The parametric equation of the line through the points (2,-4,1) and (0,4, -10) is: A. x…

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Q: The vector equation of two lines , and 4 are 1+x 2- -3+2 and 4 a-y= Given that/, and /, intersect at…

A: Solution (i): Value of a Given lines are, (1+x)/2​=(2-y)/3​=(−3+z)/4​=(r1​)(say)     .... (i)So,…

Q: Find a vector equation and parametric equations in t for the line through the point and…

A: Given that the point that posses through the line and the line perpendicular to the plane is, P 0 =…

Q: Find parametric equations for the line that passes through the point P and is parallel to the vector…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Here we find the vector and parametric equations of line.

Q: Find parametric equations for the line that passes through the point P and is parallel to the vector…

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Q: a) Find the scalar parametric equation and vector equation (r = c + ta) of the straight line z+5 x –…

A: We have to find

Q: L(t) The vector parametric equation for the line through the points (1, 2, 4) and (5, 1,-1) is

A: Given points,  (1,2,4) and (5,1,-1)

Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

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

Q: (a) Write the vector or parametric equations of the line through the point (2,0, 3) and…

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Q: An object moves in space with acceleration a(t) = 12t²i+6tj+2k. When t = 0, the object is at (1, 0,…

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Q: Find the equation of the line that goes through the point (1,3, 2) and is parallel to the line (3t –…

A: The given line equation in parametric form is x=-2+3t y=1+2t z=4+t The direction ratio is…

Q: 1. Given the points P= (2,-4,-1) and Q=(5,-4, 2) in space. A) Find the parametric equations of the…

A: 1. A> we will find the parametric equation of the line using  two points  B> EXPRESS the…

Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through the point P(3, -4, -1)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q2 a) Find the parametric equation of the line that passes by P(1, 2, 2) and that is parallel to the…

A: We have to solve above question of vector and 3D.

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) the line…

A: We have to find the equation

Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) =…

A: This is the answer of question no. 4.

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

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Q: Find the point where the graph of the vector equation r(t) = ⟨2 − 3t, −2 − t, 2 + t⟩ intersects the…

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Q: Given the parametric equations x = t1 - t2 y = 2 + 12 z = -1 - 211 + 3t2 These parametric equations…

A: Given that, the parametric equation as, x=t1-t2y=2+t2z=-1-2t1+3t2 Here, parametric equation are…

Q: Exercise 1 The parametric equation of the line through the points (2,-4,1), (2, –4,1) and (0,4, –10)…

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Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through (0, -7, 0)…

A: The given point and the plane is,

Q: a) Find the scalar parametric form of the equation of the line which is parallel to the line of…

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Q: r: A = (3,2,4) m = i +j+k 2: А %3D (2,3,1) В %3D (4,4,1) %3D (a) Create Vector and Parametric forms…

A: Let us solve the given problem related to Straight lines in Space in the next steps.

Q: Complete the parametric equations of the line through the points (7,3,-5) and (0,6,1) x(t) = 7 - 7t…

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Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to…

A: Hey, since there are multiple questions posted, we will answer the first two questions. If you want…

Q: If x = 1- 2t and y = 1+t denotes the parametric equation of a line in 2D , then (-2,1) is a) A point…

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Q: 2. Find the parametric and symmetric equations for the following lines. (a) r=i- 2j- 3k+t(i+j+k).…

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Q: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…

Q: 9. (A) Find the parametric equations for the line through the point P = (-5, -1, -3) that is…

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Q: 22. Find (a) parametric equations for the line of intersection, and (b) the cosine of the angle…

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Q: If a line is parallel to the vector li + lj+ 4k and passes through the point P = (8, 4, 8), then the…

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Q: Q1: Find the vector equation, parametric equations, symmetric equations for the line that pass…

A: We need to find the vector equation parametric equation and the symmetric equations for that line.…

Q: 5. Given the points P= (2,-4,-1) and Q= (5,-4,2) in space. A) Find the parametric equations of the…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

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Q: Find a vector equation and parametric equations in t for the line through the point and parallel to…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.