1. Find the point of intersection of the plane 3x+4y-2z=13 and the line given by parametric equations x = 1 + 2t, y = 2 – 3t, z = 3 + t, - 00

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

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Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

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Q: Which of the following is the equation of the plane that is tangent to the surface 2 x² + y? – x z –…

A: Consider the provided information, The provided surface, 2x2+y2-xz-3z=1 Find the partial derivative…

Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

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Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: -Determine the equation of the trace of this plane in the xz plane given 2x + y − z = 4.…

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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: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

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Q: 1. a) Find parametric equations of the line of intersection of the planes 3x- 2y+z=0 and…

A: Given : equation of a plane, 3x-2y+z=08x+2y+z-11=0

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: I need ass istance with this for History of math 8.4.3   I have attached how I did 8.4.2 for…

A: Given:

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

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

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: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Find the equation for the line passing through P = (2, -2, 1) and perpendicular to the plane -x + y…

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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: 3. Find the distance from P(1, 1, 1) to the plane II with equation r – 3y + 4z = 10.

A: Distance between point and plane is (4√26)/13.

Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

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

A: The objective is to find the parametric equations of the line through the point.

Q: Consider the planes 71 : x - 2y + 3z +1 = 0 and 72 : 2x + y+z+2 = 0. Let l be the line of…

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Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x-1+3t y=t z35+2t -<…

A: Two points A and B are given we have to find the parametric equation of the line segment AB. A line…

Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: The equations for the plane through p0(0,2,-1) normal to n =3i - 2j - k O 3x-3y-3z=0 O 3x-3y=z O…

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Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: The parametric equation for the line passing through P(1,1,5) and parallel to n=(0,0,1) is defined…

A: Topic = Vector

Q: 6) Consider the plane P : x+y – z = 0 in K³ that contains both the points P1(1,0, 1) and P2(-1,1,0).…

A: Given : plane P : x + y - z = 0  &amp; Points P1(1,0,1) &amp; P2(-1,1,0) To find :  1. Equation of…

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

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Q: Find an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

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Q: For planes 2x+ y – z = 2 and 2x + 3y + 5z = 4. %3D Write the parametric equations of the line at…

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Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: 6) Consider the plane P : x+y – z = 0 in R³ that contains both the points P(1,0, 1) and P2(0, 1, 1).…

A: • In the first part, we have to use the general Cartesian equation of a line passing through two…

Q: Consider the plane P :r+y-z=0 in R that contains both the points P:(1,0,1) and P:(0, 1, 1). Answer…

A: The equation of the straight line passing through 2 points is , , .  Here, the points are .

Q: Find the point on the curve of intersection of the paraboloid x² • y² + 2z=4 and the plane x-y+ 2z…

A: This question can be solved by options because we have only two equations and three variables.

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: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

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: Let P(r, y, z) be the point at which the line with parametric equations x = -t, y=3+2t, z=1-t te R,…

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Q: 13. Consider the point P(3,2,1) and the plane given by the equation 3x +2y+z=0 on the plane closest…

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Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

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Q: An equation of a plane P passes through the point (0, 0, 3) and perpendicular to the line L:x =1 –…

A: Remember that the vector (l, m, n) is parallel to the line with parametric equationx=a+lt, y=b+mt,…

Q: 20. The Cartesian equation of the plane which contains the point (1, -2, 3) and perpendicular to x-7…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

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

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Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.

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

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.