What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with the positive x-axis?

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

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Q: The acute angle of intersection of the planes x + y− 2z = 5and3y −4z = 6 is _____.

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Q: The angle between two planes is the smallest angle 0 between the planes 6x + 2y – 4z = 0 and - 7x +…

A: We will solve the problem

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: 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: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: What is the size of the acute angle formed by the x-axis and the line 3x + 2y = 12?

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Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

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

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Q: 4. Find the angle made between the two planes: r+ y - z = 5 and 2r + y +3z = -1.

A: Given that: Equation of first plane: x+y-z=5   ........(1)Equation of 2nd plane: 2x+y+3z=-1…

Q: Find the acute angle between the lines x + 2y = 7 and 5x – y = 2. %3D

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Q: Find the angle between the plane r+y-z=21 and the line r-13y+2%3D3-2z.

A: Angle between the plane and line

Q: Find the acute angle (in degrees) between the planes Sz + 3y +5z 1 and 2z

A: P1 denotes plane 1 P2 denotes plane 2

Q: Q: To find an angle between planes 2x + 4y - 4z- 6 = 0 and 4x + 3 y+9=0.

A: We have to find the angle between the given two planes.

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

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0. %3D

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Q: Find the distance between the parallel planes 2x +y + z = 0 and - 6x – 3y-3z – 13 = 0. | NOTE: Enter…

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Q: Show that the plane 2x − y − 3z = 4 is parallel to the line x = −2 + 2t, y = −1 + 4t, z = 4, and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the acute angle (in degrees) between the planes 5x 4y – 2z = 8 and 5x 2y – 5z = 5. %3D %3D

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Q: Find the angle between the planes x+y=D1 and 2x+y-2z%3D2?

A: Given planes : P1: x+y-1=0, P2: 2x+y-2z-2=0 ⇒n1⇀=i+j, n2⇀=2i+j-2k

Q: Determine the angle between the planes: x-z+7=0 2x +y-z+8 = 0

A: Solution :--

Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

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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: Find the obtuse angle formed by the lines x+3y+3=0 and x-y-2=0.

A: Topic - angle between lines We will take absolute value of angle as sign depends Up on which line we…

Q: Find the acute angle (in degrees) between the planes - 2x – 5y + 2z = 0 and 2x + 3y – 2z = 5. :-2 0…

A: The given equation in the vector form is, a=-2x-5y+2zb=2x+3y-2x Then, a=-22+-52+22=33b=22+32+-22=17…

Q: A) Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x - 2 y-z = 5

A: Given : 2x+2y+2z=3 and 2x-2y-z=5   To find: Angle between planes   we know that for plane Ax+By+Cz=d…

Q: Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x – 2 y-z 5

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Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

Q: The distance from the point P(2, 1, 0) to the plane 2x + y + 2z+ 6 = 0 is 3.7 True O False

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Q: Find the angle between two lines whose direction cosines are given by l + m + n = 0 and 1² + m² - n²…

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Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

Q: Find the angle between the two planes 4x-y+3z=12 and x+2y+4z=4. Make a sketch of your answer.

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

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Q: The length of the line segment joining the two points of intersection is 3 – x = y = 7+1 With the…

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Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: Find the acute angle (in degrees) between the planes x−4y−2z=1x-4y-2z=1 and −x+3y+z=−8-x+3y+z=-8.

A:

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 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: 8. What is the angle between the two planes x+y=0 and y-z=2?

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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: 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 angle between the lines represented by 2x2+xy-6y2+7y-2=0

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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 angle between the line 2 x+v3 : = z + 1 and the plane vZx + y + z – 2 = 0.

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

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Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: Calculate the vector normal to the yz plane. Equation of yz plane:x=0Equation of vector normal to yz…

Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0.

A: Introduction :

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.