Consider the line which passes through the point P(3, -1, -1), and which is parallel to the line x = 1+ 5t, y = 2+ 1t, z = 3+ 6t Find the point of intersection of this new line with each of the coordinate planes: ху-plane: ) xz-plane: yz-plane:

Q: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

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Q: Give the general equation of the plane containing the point (3,-1,4) and perpendicular to the line =…

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Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: Consider the line which passes through the point P(1, -3, -2), and which is parallel to the line x =…

A: Given: The vector equation of the line is: x=1+4t;y=2+7t;z=3+1t r→=123+t471 so the line is the…

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 10 — 0. - - %3D -…

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Q: Determine the general equation of the plane containing the point (1, 2, –1) and the line

A: The given equation of the line- 1-x3=y+23=z-3 It can also be written as follows- x-1-3=y+23=z-31…

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

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

Q: Which point is closest to the yz-plane? ? What is the distance from the yz-plane to this point?

A: The distance of a point from the yz-plane is given by the x coordinate of the point. Because, the x…

Q: Find the distance between the point (1, 3, −1) and the plane 3x − 4y + 5z = 6.

A: According to the question, we have to find the distance between the points 1,3,-1and the plane…

Q: Determine if the plane given by -x + 2z 10 and the line given by %3D (x = 5, y = 2 -t,z = 10 + 4t)…

A: given plane: -x+2z+10 given line: (5,2-t,10+4t)

Q: Give the general equation of a plane which has point (1,2, -1) together with line with symmetric…

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Q: Find the point of intersection of the lines 2t + 1, y = -t+ 2, z = t+ 1 and x 2s + 2, y = s+3,z =…

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane…

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or…

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

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Q: Consider the line which passes through the point P(-5, -5, -4), and which is parallel to the line x…

A: The vector equation of the line is given by: x = 1+5ty = 2+7tz = 3+1tr→= 123+t571So the line is in…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: 7x + 3y + 4z = 5, and 21x + 9y +12z = 13

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Q: Find the plane determined by the intersecting lines.

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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: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

A: We will solve the problem

Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (-1,-6, 5)…

A: Given: Equation of line as, l:(x,y,z)=(-1,-6,5)+n(1,3,-2) And the equation of the plane is given as…

Q: Consider the line which passes through the point P(-2, 4, 3), and which is parallel to the line x =…

A: Consider a line  L1:x=1+7t,y=2+7t,z=3+4t Point : −2,4,3

Q: You are given the following points: A = (-4, 20, 16), B = (20, 0, 7), C = (8, –15, – 19). %3D Which…

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

Q: the plane whose intercepts with X zagy = b,Z=C show that the Coordinate axes are has equation Ą + +…

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Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Show that the planes are orthogonal.

A: Given: 3x+6z=12x+2y−z=3

Q: 4. Find the equation and sketch the graph of a plane that is parallel to the yz-coordinate plane and…

A: We know that equation of plane parallel to yz-coordinate plane is given by: x=k where k is some…

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

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Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: What is the distance between the point A(1,-1,3) and the plane x + 2y + 2z + 1=0 ?

A: To find The diatance between the point A(1,-1,3) and the given plane

Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7)…

A: Given: Parametric equation of line l: (x,y,z)=(3,-1,7)+r(-5,2,1) Equation of plane: 2x+3y+4z=24

Q: The planes 3x + 6z line. = 1 and 2x + 2y - z = 3 intersect in a a) Show that the planes are…

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Q: Check that the line (1,0,1)+t(3,0,1) is parallel to the plane -2x+4y+3z=13 and calculate the…

A: For the equation of the plane , the direction vector of the normal to the plane is given by . For…

Q: Find an equation of the plane through (-8, 4, –9) that is perpendicular to the planes 5x – y +z = 1…

A: Solution of question is written in below steps.

Q: Find the point at which the line (0, –3, 5) + t(4, –1,2) intersects the plane 4x + 4y – 4z = 0.

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Q: Find the distance of the point (3,8,2) from the line x-1 -y+3 -z+2 measured -3 2 -4 parallel to the…

A: Given point 3, 8, 2Given line - x-12=-y+3-4=-z+2-3Let the parameters be equal to an arbitrary…

Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

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Q: Which of the points A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) is closest to the yz-plane? Which…

A: Given- A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) To do- 1.Which of the points A(−4, 0, −1), B(3, 1,…

Q: Does the line given by x = 9 + 21t, y = - 7, z = 12 - 11t intersect the xz - ?plane yes No

A: As per bartleby guidelines we only give first one question answer.

Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Equate the x and y coordinates in t and s domain to obtain values for t and s.

Q: What is the intersection of the plane x+2y-z=0 and the line (x.y,z) = (2,2, - 3)+ k(4,–1,1), kER?…

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Q: Find the distance between the point (1, 0, 2) and the plane 2x − 3y + 6z = 6.

A: To find the distance

Q: Are the plane 2x-y-4z 10 and the line {x = 2+4t,y 5- 2t,z =-8t} parallel or orthogonal?

A: We have to find out

Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.