a) Find the best straight line fit to the given data points (-3,7), (1,–1),and (3,–7). b) Find the parametric equations for the line in which the planes x+4y-2z=2 and 3x – y+2z =4 intersect.

Q: 3. The plane in ' with equation 4x=34 %3D

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Q: Find parametric equations for the line of intersection of the planes x + 2y + 3z = 4 and 5x + 6y +…

A: Given: x+2y+3z=4   and  5x+6y+7z=8To obtain the parrametric…

Q: 2) Find the parametric and symmetric equations for the line through (1, –1, 1) and parallel to the…

A: Solved below

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: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: Find parametric equations for the lines in The line through (2, 4, 5) perpendicular to the plane 3x…

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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: Find a parametric equation for the line that passes through points A (3,-2,4) and B (5,6,-2). x = 3+…

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Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

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Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Find parametric equations of the line through (-1, –1, 6) that is parallel to 2i – 4j+k. x(t) = y(t)…

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Q: Find the Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

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Q: Find an equation for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

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Q: Find the distance from the point (-2,0,3) to the plane given by the equation 3x+4y 5.

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Q: Find parametric equation of the line joining points P{(2,4, –1) and P2(5,0, 7). Where does it…

A: To do this we need the vector V→ that will be parallel to the line. This can be any vector as long…

Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1:2x – y…

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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 the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: Line of intersection

Q: Find parametric equations for the line through the points P(-1,- 1, -4) and Q(-4,-7,7). O A. x-t-3 y…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

A:

Q: Find parametric equations for the line through P0 = (3, −1, 1) perpendicular to the plane 3x + 5y −…

A: A line L in sace with direction vector d=d1,d2,d3 that asses throughthe point P=(x0,y0,z0) can be…

Q: Find an equation of the plane containing the points P(O,0,o) and Q(2,2,2) and parallel the line…

A: Given:- Equation of line x= t, y = 1,z= t  To find:- An equation of the plane containing the points…

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 an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: Find parametric equations for the line containing the points P(0,2,0) and Q(1,3,5).

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Q: Find parametric equations for the lines in The line through (0, -7, 0) perpendicular to the plane x…

A: we know that equation of line in parametric form which passes through pointx1,y1,z1 and…

Q: Find the parametric equation of the line of intersection of two planes correctly: P1:x+3y+5z=0 and…

A:

Q: Find the distance between the point P(-1, 2, -1) and the plane 2x + 6y - 9z + 1 = 0.

A: Use formula to calculate distance

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 equation of a plane through the point (3, -2, 8) and parallel to the plane z=x+ y.

A: Given, Plane is passing through the point (3, -2, 8) and Parallel to the plane z=x+y    Equation of…

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: What is the parametric equation for the line through the point (1,2,3) parallel to the y- axis? (a)…

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Q: Find parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x –…

A: Cross product of normals of planes is normal to the required line of intersection

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

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

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Q: 2. The plane with equation: 7 = (1,2,3) + m(1,2,5) + n(1,–1,3) intersects the y- and z- axes at two…

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Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

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Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x -…

A:

Q: Find parametric equations for the line segment joining the points (-6, 7) and (4, 5). x=7-2t, y…

A:

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: 2)as per our guideline we have to write one question at a time kindly repost remaining questions

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 distance from the point B = (1,0, 2) to the plane 2P whose general equation isx + y - z =…

A: Given: equation of plane is x+y-z=1  We know that distanced from the pointx1,y1,z1 to the…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.