The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB          So the distance from P=(4,1) to the line through the points A=(0,−3) and B=(3,−2) is

Q: Choose a set S of three points such that aff S is the plane in R3 whose equation is x3 = 5. Justify…

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Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

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Q: 2. Give the symmetric equations of the line l perpendicular to the plane T : 5x– 2y = z+4 and…

A: we have to find equation of line.

Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

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Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: 13. Find the distance between the two given parallel planes. x+y-3z = 4 x+y-3z=12

A: Given that:

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: 5. The ends of the transverse axis are at (+8,0) and the ends of the conjugate axis are at (0. 16).

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Q: Find an equation of the plane. The plane that passes through the point (1, -1, 1) and contains the…

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Q: 2. Find an equation of the plane parallel to the line

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: Let Q(0,-1,1) be a point in space and let u have the line L whose equation is L: 3- 3x = 1 – 3 y…

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Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

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Q: Find the equation of the plane with the given description. Passes through P = (3, 5, −9) and is…

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Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

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Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

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Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: We know that the equation of a line passing through the point a and parallel to the vector b is…

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

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Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

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Q: Find equation of Plane teter mined by the Lines Li. X = t-29 y = 2t+3 Z= +4 and Lz! X…

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Q: Find equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

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Q: Find an equation of the plane through (1,3,–2) and the line of intersection of the two planes with…

A: Given that, Point A (1,3,-2) Two planes  P1: x-y+z-1=0P2: x+y-x-1=0   We have to find the equation…

Q: Find the general equation of the plane perpendicular to the line Z – 2 y+ 4 1- x = 3 and is 3…

A: This is a problem of vector algebra and geometry.

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

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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– 2t,…

A: Given,          An equation of a plane P passes through the point 0,0,3 and perpendicular…

Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 0, 1), and R(1, 1, 0).

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Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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Q: Find the distances (a) Between l1 = (2+ 2t, –1+t, -3t) and l2 = (4, -5 – 3t, 1+ 4t) (b) Between the…

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Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: Planes as:                       2x+y-z=3x+2y+z=2;   The given point as:                        (1,…

Q: Find the plane determined by the intersecting lines. L1 x= - 1+ 3t y =2 +3t z =1- 4t L2 x= 1-4s y =…

A: Given :-  The plane determined by the intersecting lines. L1    :   x = -1 + 3t    ,    y = 2 + 3t…

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: 2. Find the equation of the line that is parallel to the intersection of planes 12, 2x-8y + z = 0…

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Q: Q2 / A man moved from the point (2, -2, 1) to the point (8, 3, 4). Express the displacement moved by…

A: The given point is                    P1 (2, -2, 1)  and  P2 (8, 3, 4) To find displacement in terms…

Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

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Q: (i) Find the distance from the point P(-1, 2, 1) to the plane II1 : 2x + y – 3z= 4. (ii) Find an…

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Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

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Q: Find the acute angle of intersection of the planes x + 2y – 2z = 5, 6x – 3y + 2z = 8 to the nearest…

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