Question 1. of the line L that passes through the points (-1,3, 7) and (2, –1,3). (a) Find the vector, parametric and symmetric (b) Find the point where the line L intersects the XY-plane.

Q: 3 2) Determine the vector, parametric and cartesian eguation ef the line passing through-the…

A: Given: Passing point P0(1,3,2) Parallel vector V=(1,1,1)

Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

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Q: If a line is parallel to the vector 8i + 5j + 3k and passes through the point P = (6,2,4), then the…

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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: Find the parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

A: Topic = Vector

Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

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Q: Question 19 Let L be the line passing through the point P-(-1, 2, 2) with direction vector d-[1,-2,…

A: First find the equation is line by given points and direction.  Then assume it T and convert (x,y,z)…

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t y…

A: Given, The parametric equation of the line D passing through A and parallel to vector v is  x =…

Q: Given a point M = (5,–3,–2) on a line in space and a parallel vector to the line defined as vector d…

A: Parametric equations of a line  in 3-D space are given byx = x0 + t a , y = y0 + t b , z = z0 + t c…

Q: Find parametric equations of the line that is perpendicular to both i = (1,0,0) and i = (1,1,1) that…

A: Given that: i=<1, 0, 0>v=<1, 1, 1>and P(1, -2, -1)

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

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

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Q: Find the parametric equation for the line in R' that passes through the point (1, –2, 3) and that is…

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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: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: QUESTION 3 Let r(t)=(1-t?,5t,2t3). r'(3). Find the z-component of the vector

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Q: 1 - Find a vector equation and parametric equations for the line segment connecting P(a, b, c) and…

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Q: 1. Find both the vector equation and the parametric equations of the line through (−3​,5​,6​)and…

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Q: Questions 1 - 5. Consider the plane that goes through the point (4, 1, 3) and is orthogonal to…

A: Given that the plane that goes through the point (4,1,3) and is orthogonal to vector (2,3,1) . Here…

Q: Find the parametric equations of the line contains point P (2, -1, 2) and tangent to the vector v =…

A: Given problem:- Find the parametric equations of the line contains point P (2,-1, 2) and tangent to…

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2 + 3t…

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Q: Find the vector and parametric equations for the line through the point P = (-4, –4, 5) and the…

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Q: (S'34) 9uq Find vector, parametric, and symmetric equations of the line through (2,3,4) and is…

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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: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

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Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A: We have to find the equation of the line passing through the point (1,2,-1) and normal to the plane…

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: 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:   a) the parametric equation of the line determined by points A(1,0,2) and B(2.2.1). b) the…

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Q: Please answer the following question: Find the distance of the point (2, 6, –4) from the line r(t) =…

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

Q: If a line is parallel to the vector 3i + 2j + 1k and passes through the point P = (1,3, 8), then the…

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Q: If a line is parallel to the vector 3i +2j+ 1k and passes through the point P = (1,3,8), then the…

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Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: Find the vector and parametric equations for the line through the point P= (3,0, –1) and the point Q…

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Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: (a) Find a parametric equation and symmetric equation of the line that pases through the point (2,…

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Q: Give a vector parametric equation for the line through the point (−1,−1) that is perpendicular to…

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

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Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

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Q: 23. x = 1, y = 1/(1 + 1²),

A: Solution: The objective is to sketch the curve with the given vector equation

Q: 47. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: We’ll answer the 47th question since we answer only one question at a time. Please submit a new…

Q: Find the distance of the point (2, 6, –4) from the line r(t) = (-1 + 31, –1+41, 5 – 2t). Give a…

A: Consider the given point as, 2,6,-4  And the line -1+3t,-1+4t,5-2t

Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

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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: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…