Check the alternative that contains the points of intersection of the line r below with the coordinate planes: r: {y=3x+3 {z=3x+6

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z ] = [− 1, − 9, 16]+t…

A: The given line is [ x, y , z] = [ -1, -9, 16]  +  t   [ 3, 3, -5]  and the given plane is x+4y+3z=11…

Q: Q5) the value of the constant a for which the line x=2+t,y=2+3t,z=3+t and the plane ax+y-2z-7=0 are…

A: We will use definition.

Q: Find r so that the line through (2,6) and (-4,r) a).parallel to 2x-3y=4 b). Pendicular to x+2y=1

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Q: Find the intersection of the line and the plane. x + y + z = 14, r(t) =〈1, 1, 0〉+ t〈0, 2, 4〉

A: Given that, The equation of the line is: x + y + z = 14 And, the equation of the plane is:  r(t)…

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

A: Answer

Q: Find the point of intersection of the lines: y = 4x + 1 and y = -2x +4 %3D o (2,9) 으(4,2) ㅇ (4,3) O…

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Q: find the value of y such that the points are collinear  (5,5) (-1,y) (2,4)

A: if three points are collinear then it means they cannot form a triangle so the area of triangle in…

Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: Find equation of the plane that contains the lines L,:x 3+5t, y = 6+2t, z = 7t and L2: x = 7t, y =…

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Q: Find the point (if it exists) at which the following plane and line intersect. -2x-10y-10z = -19 and…

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Q: the distance from the point P(2,3) to the line -3y=-4x is : * 1/5 - 1/5 غير معرفة 1/25 17/5

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Q: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

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

A: we have to find the point of intersection of the given lines

Q: ) Find the equation of line of intersection of the following planes 3x – 4y + 4z – 29 = 0 , 6x – 8y…

A: Explanation of the solution is given below...

Q: Q4:Show if the line (x = 5y +17, y+z-2= 0) lies in the plane 3x-41y-26z +1 = 0 or no ? Where does…

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Q: a) Find the equation of line of intersection of the following planes 3x – 4y + 4z - 29 = 0 , 6x – 8y…

A: As per guidelines we are allowed to solve one question at a time. Kindly repost the rest question…

Q: 6x Find -dA, where R is the parallelogram enclosed by the lines 4x – 3y 6x – y = 0, 6x – y = 9, – 4x…

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Q: Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r,…

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Q: H.W 2- Determine the points of intersection of the given line and the three coordinate planes. 1. x…

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Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: Find the distance from the point Q= (2,2,2) to the line of intersection of the planes x+y+z=1 and…

A: Distance from the point Q(2,2,2) to the line of intersection of planes x + y + z = 1 and x + y = 2

Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: -62-y Find dA, where R is the parallelogram enclosed by the lines -3x +y R - 6x – y = 0, - 6x – y =…

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Q: Evaluate (r + y)e**-v° dA, where R is the rectangle enclosed by the lines r – y = 0, x – y = 2, x +…

A: Given: The double integral   ∬(x+y)ex2-y2dA  enclosed by the region x-y=0,   x-y=2,  x+y=0    and…

Q: Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining…

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Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z][-1, -9,16]++[3, 3,…

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Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: Determine whether the line L: = 3- 2t, y=4+ 2t, z = 5+ 2t. is parallel to the plane a-y+3z 7.

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Q: Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining…

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Q: Find the value of y such that the points are collinear. (1, -2), (-5, y), (-2, –5) y = %D

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Q: Find the line of intersection of the planes 2x – y + z = 2 and x + 2y – 4z = 1

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Q: find the point in which the line meets the plane x = -1 + 3t, y = -2, z = 5t; 2x - 3z = 7

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Q: d the condition for the point (a,0),(h,k),(0,b) when ab is not equal to 0 to be collinear

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Q: Determine whether each point lies in the plane.  2x + y + 3z − 6 = 0 (a) (3, 6, −2)    (b) (−1, 5,…

A: Given- 2x+y+3z-6=0 To find-  whether each point lies in the plane and the points are (a) (3, 6, −2)…

Q: Q5. Find an equation of the plane that is parallel to the line of intersection of the planes (x+…

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Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

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Q: Determine the intercepts of each plane. a) [x, y, z] = [1, 8, 6] + s[1, –12, –12] + t[2, 4, -3]

A: As per policy, only the first question is answered as you have asked multiple questions asked in a…

Q: Find the equation of the line where planes Q and R intersect. Q: x-3y+2z=1 R: x+y+z=-1

A: To calculate the equation of line from the point of intersection of the planes Q and R. Where, the…

Q: Find the coordinates of all points (x, y) that lie on the line whose equation is 2x + y = 8, so that…

A: Given: The coordinates of all points x,y that lie on the line whose equation is 2x+y=8, so that the…

Q: Determine the points of intersection of the given line and the three coordinate planes. x =1+2,y…

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Q: Select all lines that are perpendicular to y -4 =- (r+1) O y = +8 O 3r 2u- 2

A: The given line is y-4=-23x+1 ............................ (1)  Compare with,

Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: find the point in which the line meets the plane x = 2, y = 3 + 2t, z = -2 - 2t; 6x + 3y - 4z = -12

A: The equation of plane is 6x + 3y - 4z = -12. The coordinates of the line is x = 2, y = 3 + 2t, z =…

Q: Determine the points of intersection of the given line and the three coordinate planes. x =4-2, y…

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Q: The midpoint of the line segment between P1 (x,y) and P2 (-2,4) is Pm (2,-1). Find the coordinates…

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Q: 5- Find the distance from the point to the line. a. (0,0, 12); x = 4t, y = -2t, z = 2t b. (0, 0, 0);…

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Q: Q1/The line joining origin and point of inter section of the lines (x = 1 + 2t, y = -3 + 4t, z %3D =…

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Q: Q5. Find an equation of the plane that is parallel to the line of intersection of the planes (x+ 3y+…

A: We can find the angle between two vectors as below.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.