Consider three points in three-dimensional space: A = (15, 2, –3), B = (2, –3, 15), C =(-3, 15, 2) Find the parametric equations of the line passing through point B in the direction of AC Use t as the parameter.

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

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Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

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Q: Find a set of parametric equations for the line passing through the point (2, 0, 9) that is…

A: a set of parametric equations for the line passing through the point (2, 0, 9)  that is parallel to…

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: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

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Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

A: Given :                y = 2 x - 5  ,  t = 0        at point (3,1)

Q: Complete the parametric equations of the line through the point (-6,0,-8) and perpendicular to the…

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Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

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Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: Find a parametric equation for the line through the point (-1,-1,2) and perpendicular to the plane…

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Q: Sketch the parametric curve of the given parametric equations and indicate the orientation. 1. x=3t…

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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

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: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

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Q: Find parametric equations for the line segment joining the points (9, 8) and (16, 11). O x=9+7t, y…

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Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

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

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Q: Find the parametric equations of the line r = ⟨1, 2, 3⟩ + t(4, 0, -6⟩.

A: Given: r→=1,2,3+t4,0,-6 for any given vector equation of line r→=a,b,c+tp,q,r, parametric equation…

Q: Find the parametric equations of the line perpendicular to l1 and l2 that contains the point (-1.…

A: We have to find equation of a line which is passes through the point (-1,-1,-1) and Perpendicular to…

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: Consider three points in three-dimensional space:…

A: We have the given points  A=(11,2,−3),B=(2,−3,11),C=(−3,11,2) Now the direction ratios of the line…

Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

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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: Consider the point (−6, 2, 2), line l : (1 − x)/7 = y − 3 = z/2. Find parametric equations of the…

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Q: Which of the following is Parametric equations for the line passing through the origin and A(1, 0,…

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Q: Find the parametric equation of the line that passes through the point (4, -5, 0) and is…

A: We have to find the parametric  equation of the line.

Q: Match the parametric equation with the corresponding plane curve displayed. Sx=47-5 y=16 130 104 78…

A: The given parametric equation is: x=4t2-5y=16t4

Q: Complete the parametric equations of the line through the point (4,-8,3) and perpendicular to the…

A: See this solution in below

Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

Q: Complete the parametric equations of the line through the point (3,-7,-2) and perpendicular to the…

A: Given that, the equation of the plane is     -3x-y+z=2  and the point (3,-7,-2) The direction vector…

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 the parametric equations for the line through the point (5, 2,9) and perpendicular to the plan…

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Q: Suppose parametric equations for the line segment between (0,-10) and (8,-1) have the form: a + bt y…

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Q: Complete the parametric equations of the line through the point (-3,1,-4) and perpendicular to the…

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Q: Find the parametric equations for the line passing through points P(2, -3, 1) and Q(4, 1, -4)

A: Given points are  P2,-3,1,Q4,1,-4

Q: Find a set of parametric equations to represent the graph of the rectangular equationy = 3 − x2…

A: Given:  rectangular equation:  y=3-x2 ...(1)(a)…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: Find a set of parametric equations for the curve of intersection of a paraboloid x² + (y − 2)² = z…

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Q: What is the parametric equations of the line through (2,2,2) parallel to the x- axis ? a) x = 2, y =…

A: 7) The Parametric equations of the line through (2, 2, 2)  parallel to x-axis is given…

Q: Find two different sets of parametric equations for the rectangular equation  y = 4x + 1, t = −1 at…

A: Given equation is y=4x+1, t=-1 and the point is (-2,-7).

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: Provide parametric equations for the line passing through the coordinates (1, −3, 2) and…

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Q: Find the parametric equation of the line of intersection of the planes 2x+y-z=1 and x-2y+3z-9

A: First find cross product take normal vector useformula

Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.