1.Find the vector equation and parametric equations of the line passing through the point P(5, 6, 7) and parallel to the line with parametric equations x = -6 + 2t, y = 3 + 3t, z = 5 + 4t.

Q: Find the vector and parametric equations for the line through the point P(4, -2, -4) and parallel to…

A: Find the vector and parametric equations for the linethrough the point P4,-2,4 and parallel to the…

Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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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: Find parametric equations of the line through (-1,0,3) that is parallel to 5i – 6j+k. x(t) y(t) =…

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Q: 3. Find a set of parametric equations for the line of the intersection of the planes 3x-3y-7z -4 and…

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Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

Q: Can someone help me out with this question?

A: On a horizontal line, the y value is fixed.  And x values are changing.

Q: Find parametric equations for the line pass- ing through the point P(2, –1, 4) and parallel to the…

A: Given, The line is passing through the point  P 2, -1, 4  and parallel to the vector 1, 4, -2. We…

Q: Find the set of parametric equations of the line through the point (1, 6, 3) that is parallel to the…

A: The direction ratio of the line x=6+5t, y=6+2t, z=4+2t is (5,2,2). Parallel lines have the same…

Q: Find the parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

A: The parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

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: Find the vector and parametric equations for the line through the point P(-5, 3, -1) and the point…

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Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

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

A: Line passing through the point 6, -6, 8 and perpendicular to the plane 7x+2y-3z=-8. Since the line…

Q: Find both the vector equation and the parametric equations of the line through (-3,3,7) and (3, -…

A: Consider the points <-3,3,7> and <3,-1,0>. The vector equation and the parametric…

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

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) and (5,2,4),…

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4…

A: This is the problem from the vector algebra and 3D geometry.

Q: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

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

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

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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: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

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

A: The parametric equation of a line passing through the point and has a direction cosines <a , b…

Q: Determine the parametric equations of the plane containing the point (1, -5, 9) and the line [x, y,…

A: I am going to calculate the parametric equations of the plane containing point (1,-5,9) and the line…

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

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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: 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 equations for the line through the point (1, 7, 2) that is parallel to the plane…

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Q: Find the parametric equations of the line containing the point (-2,1,2) and parallel to the vector…

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

A: The solution is given below in the next step:

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: 1. Find the vector and parametric equations for a line passing through (7,-4, 2) and parallel to the…

A: We have to find the vector and parametric equation of the line

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Find parametric equations for the lines in The line through (1, 1, 1) parallel to the z-axis

A: Given: 1,1,1 parallel to z-axis

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

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Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

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: y+3x-6z=8

A: answer is in next step

Q: 7. Find the parametric equations of the line passing through A(1, -2, 6) and which is perpendicular…

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Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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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 a set of parametric equations for the line passing through the point       (1, 0, 2) that is…

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Q: Find parametric equations for the line described below. The line through the point P(1, 1, -2)…

A: Use equation of parametric line and put value

Q: Find a vector parallel to the line defined by the parametric equations x(t) - 3 – 9t y(t) 2 + 7t…

A: Need to find parallel vector and point on the line

Q: The line L is parallel to the plane x+y+z=2 and is perpendicular to the vector (-1,1,–2). If the…

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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.