6) Find the following: a) An equation of the plane passing through the points P(2,1, 10, Q(-1, -1, 10), and R(1, 3, -4) b) The parametric equations for the line through Q that is perpendicular to the plane in part a.

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: 4. The planes 1 and 1, are have cartesian equations x – y + z +1 = 0 and 2x + y – z – 1 = 0…

A:

Q: Let A : x + 2y – z, B be the plane passing through the points (2, 1, 2), (1, 1, 3), (2, -1, 1), and…

A:

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

A:

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

A: A parametric equation of a line can be written if a point on the line is given and a vector parallel…

Q: Determine the parametric equation of the plane that contains the line y-3 *+2-³-² and the point…

A: Virtual find the standard form of the plane then by satisfying the parametric values we will…

Q: Find parametric equations of the line through (-3,0, 3) that is parallel to 5i– 7j+k.

A: Recall:  The parametric equations of the line through (x0,y0,z0) that is parallel to a i+b j+c k is…

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

A:

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

A:

Q: 1: Find the angle between the planes 3x - 6y + 4z 3 and 2x - 2y +z = 4 then find the parametric…

A:

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

A:

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

A:

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: 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 (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: How do you find the parametric and symmetric equation of the line passing through the point (3, 2,…

A: We have to find the parametric and symmetric form of the line perpendicular to the given plane at a…

Q: Consider three points in three-dimensional space: A = (15, 2, –3), B = (2, –3, 15), C =(-3, 15, 2)…

A: The parametric equation of a line passing through the point and in the direction of  is defined by…

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: 4. (a) Find a parametric equation and symmetric equation of the line that pases through the point…

A: We have a point P(2,-1,3) and a vector  i^+2j^-3k^ We have to find a parametric equation and…

Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: We have to find a set of parametric equations of the line with the given characteristicsThe line…

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

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

A:

Q: Derive the parametric equations of the line of intersection of the two planes: II : 2x – y + 2z = -1…

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…

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

A:

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

A:

Q: 7. Find the vector and parametric equations of the plane that is parallel to the yz-plane and…

A: W e have to find the equation of plane.

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: 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: (s) (a) Find a parametric equation for the line through (2, 4, 6) that is perpendic- ular to the…

A: Equation of line in 3D

Q: Find a set of parametric equations and symmetric equations of the line ` con- taining the point P(1,…

A: Given Point is (1,-2,3) And Plan is : 2x-y+3z=6

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

A:

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

A:

Q: Example 6: Determine whether the planes 3x+ y- 4z = 3 and -9x-3y+12z= 4 are | orthogonal, parallel,…

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

A:

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: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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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: Find parametric equations for the line through Po = (3, -1, 1) perpendicular to the plane 8x + 5y –…

A: Consider the point Po and the equation of the given plane. Find the vector Po and the direction…

Q: B Find the parametric equation of the plane passes through the point (-3,0,7) and perpendicular to…

A:

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

A:

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: 2) Determine an equation for each of the following planes given the indicated form for each…

A:

Q: 1. a. Given the points A(1, 2, 4), B(2, 0, 3), and C(4, 4, 4), i. determine the vector and…

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Q: Find the equation for the plane that passes through (2,4,-1) and contains the intersection of the…

A: The plane equation Ax+By+Cz+D=0 passing through three points x1,y1,z1, x2,y2,z2 and x3,y3,z3 is…