The planes 3x + 6z line. = 1 and 2x + 2y - z = 3 intersect in a a) Show that the planes are orthogonal. b) Find the equation for the line of intersection.

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

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Q: Find two di¦erent planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t . Write…

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Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: Determine whether the statement " If two lines L1 and L2 are each parallel to a plane, then L1 and…

A: Two lines  L1 and L2 can be perpendicular to each other and be parallel to the same plane at the…

Q: Find the distance between the parallel planes 2x – y + 3z = 6 and 4x - 2y + 6z = 24 %3D %3D

A:

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t. Write…

A: Given:

Q: On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest…

A: Given planes, y+2z=12andx+y=6 Consider the point of intersection be x,y,z.

Q: Show that the planes given by y − 7z = 16 and 2y − 14z = 5 are parallel, and find the distance…

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

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Q: To find the equation of a plane which cuts intercepts a, b, c res- pectively on the axes of…

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Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 – t, z = 3 + 2t. Write…

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Q: Write the intersection of plane UVYZ and plane SVWZ? T.

A: given figure is pointed by vertices S, T, U, V, W, X, Y, Z

Q: Which is the fourth point on plane TSW? T. U O Y

A: A plane is a 2-dimensional surface. It can have an infinite number of points. A plane is composed of…

Q: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

A: Given: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

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: 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: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

A: Let M be a plane that contains the point with coordinates -2, -2, -1 and is orthogonal to the vector…

Q: is the line x = 1 - 2t, y = 2 + 5t, z =-3t parallel to the plane 2x + y - z = 8? Give reasons for…

A: Given,

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

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

A:

Q: Find the plane determined by the intersecting lines.

A:

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

A: Given,

Q: what is the intersection of plane  x+2y+z=0 and the line (x,y,z)=(0,1,2)+k(–1,1,2), KER(real…

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Q: Hiwed Find equations for_thefallawing lines - The line through (3, Sz=2) Perfendiculor toX-z plane

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Q: Verify that the two planes x − 3y + 4z = 10 , x − 3y + 4z = 6 are parallel and find the distance…

A: Verify that the two planes x − 3y + 4z = 10 , x − 3y + 4z = 6 are parallel and find the distance…

Q: P, Q and R Find a plane that contains S and is parallel to the plane that contains the points

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

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: Make a sketch of two parallel planes intersected by a third plane that is not parallel to the first…

A: To draw the sketch of two parallel planes intersected by a third plane that is not parallel to the…

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: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

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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: Find the distance between the parallel planes −3x+y+2z=−4 and 6x−2y−4z=1?

A:

Q: he intercepts of the plane given by

A: Intercepts of the plane are (3,5,3).

Q: Find the angle between the planes (x+y+za1)and. (x-24+32-1). And find the Symmetricequations for the…

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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: Find a plane that contains S and is perpendicular to the plane that contains the points

A:

Q: Find angle between two planes given by 2x + y – z = 29 and 3x + y + 2z = 6. %3|

A: we have to find the angle between the two planes given by 2x+y-z=29 and 3x+y+2z=6. the equations of…

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

A:

Q: between the point and the plane. 43. (1,−2, 3); 2x − 2y + z = 4

A: Given: The point is 1,-2, 3 and the equation of the plane is 2x-2y+z=4 To find the distance between…

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: Suppose that II1 and II2 are parallel planes in R³, given by: II : ajx + biy +cjz = d1, and II2 :…

A: If ∏1: a1x+b1y+c1z=d1 and ∏2: a2x+b2y+c2z=d2 are parallel planes, then, the cross product ∏1×∏2=0.…

Q: P, Q and How far is the point S from the plane that contains the points R?

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Do two distinct lines in space determine a unique plane? Explain.

A: Yes ,  two distinct lines in space determine a unique plane

Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…

Q: x + 13y + 7z = 4, and 2x + 26y + 7z = 8

A:

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

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.