Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to the line x =-3 + 2t, y = 3t, z = 1 + 4t.

Q: Verify that the two lines are parallel and find the distance between the lines. L1:   x = 2 − t,   y…

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Q: 2. Find the equation of the plane containing the lines L1: (x-2)/2 = (y+1)/-1 = z/3; L2: (x+1)/2 =…

A: Given that:L1: x-22=y+1-1=z3L2: x+12=y-1=z+23

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

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Q: show.. that the line in.which. the planes.X+zy-223D5 and. 5X-zy.-7=D0.jntersect.is. pavalle.to. the…

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Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

Q: Find the point where the line x = 8/3+ 2t, y = -2t, z = 1 + t intersects the plane 3x + 2y + 6z = 6.

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Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

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Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Verify that the lines are parallel, and find the distance between them L1: x = 2 - t, y= 3 + 4t, z =…

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Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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Q: Find the distance between the given parallel planes: (a) 2x - 3y + z = 4 and 4x - 6y + 2z = 3 (b)…

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Q: Show that the distance between the parallel planes                                          ax + by…

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Q: At what point does the line: L: x=-1, y= 10 + 31, z= 4 +3t im plane 1:x- 2y + 5z + 16 = 0?

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Q: 3. Show that the lines L1 : x = 2+t, y= 2+3t, z = 3+t and L2:1 = 2+t, y= 3+ 4t, z = 4 + 2t…

A: L1: x =2+t , y= 2+3t , z= 3+t  L2: x =2+t , y= 3+4t , z= 3+t

Q: 2) Determine whether the lines 1: x = 1+ 2t, y = 3t, z = 2 – t and l2 : x = -1+ s, y = 4 + s, z…

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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: 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: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Find the equation of the line that contains the point (1,–1, 2) and is perpendicular to the plane 2x…

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Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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Q: Find the point(s) of intersection (if any) of the plane 2x + 3y = 10 and the line (x − 1)/3 = (y +…

A: The equation of line x-13=y+1-2=z-3=r(arbitarary point) then x = 3r +1 y = -2r -1 z = r+3

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: Find the intersection of the line and the plane. 2x + y = 3, r(t) =〈2, -1, -1〉+ t〈1, 2, -4〉

A: We have to find the intersection of the plane 2x+y=3 and the straight line r(t)=2,-1,-1+t1,2,-4

Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

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Q: Find an equation of the plane that contains the line x = −2 + 3t , y = 4 + 2t , z = 3 −t and is…

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Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

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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: 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 the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: Find an equation of a plane through the point (0,−2,1) which is orthogonal to the line…

A: The equation of a plane passing through the given point is as follows.

Q: Find an equation of the plane through (4, 5, 7) that is - 2 = 5t, y +3 = 10t, z = -5t. perpendicular…

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Q: Find the distance between the two straight lines and x=1+1, y=2, z= −1+2+ x=2-t, y=3t4t, z=2t at the…

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Q: Find the point at which the line (-4, –5, 2) + t(-4, 3, –5) intersects the plane 2x + 5y + 4z = -6

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Q: Find general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

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Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

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: -6x - Find dA, where Ris the parallelogram enclosed by the lines -3x+y R – 6x – y = 0, – 6x – y = 2,…

A: I have used jacobian to solve the area of above double integral.thanks

Q: B. Show that line -- is parallel to plane x-2y+z = 6

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Q: Show that the plane whose intercepts with the coordinates axis are x = a, y =b, z c has equation :…

A: Consider an equation of plane as It is given that the intercepts of plane are x=a,y=b and z=c. So,…

Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: Find an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

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Q: Find an equation for the plane parallel to the line x = 1 − 2t, y = 2 + 3t z = 1 + 2t and that…

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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: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

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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: 4:x 3+6r, y =-2+9t,: =1-12t and L:x=-1+4t, y 3+6,-8r

A: We are given L1: x=3+6t, y=-2+9t, z=1-12t. So, L1: x-36=y+29=z-1-12. Thus, a1=6, b1=9, c1=-12. We…

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: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3- 2t ,y=-2t+1,z=t is

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

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.