Let a and b be real numbers. Let L be the line defined as L:z = 5 - 5t, y= -9+t, z = a + bt, tER Let D be the plane defined as D: 6z + 4y + z = 10. Suppose that • Lis parallel to D. The distance between L and D is /53. i) Find b. i) Find the set of all values of a.

Q: Let c1= ((c1x,c1y), r1) and c2= ((c2x,c2y) , r2) be two circles and p = (px,py) be a point. Decide…

A: As per the above, we aim to determine the relationship between a point and two given circles, and…

Q: Let a and b be real numbers. Let L be the line defined as L:x = 5 – 5t, y = -9+t, z = a + bt, te R…

A: Here we will evaluate required values.

Q: Let a and b be real numbers. Let L be the line defined as L:x= 5-5t, y= -9+ t, z=a+bt, t e R Let D…

A: Solve by  formula of 3D geometry

Q: 26. Which of the following planes are identical, which are parallel to each other, and which are…

A:

Q: The line whose equation is given as: (x-2z-2=0, y-22 -0) intersects the plane (x-2y+2-1-0) at the…

A: Given: x-2z-2=0 y-2z=0 equation of plane x-2y+z-1=0

Q: 5. Find the point of intersection of the given plane and line. Plane: 2x - y+3z=7 Line: x=-1+t y…

A: We have to find  point of intersection .

Q: The planes x - 2y + 32 - 3 =0 and 3x + y - z + 5 =0 are perpendicular. Select one: True False

A:

Q: Let ℓ be the line with the equation x + 3 = y/2 = z and let P be the point (1, 0, 1). Consider a…

A:

Q: 1. Find the angle between the lines L,:x = 3 + 8t, y = -6t,z = –7+ 24t and L2:x = 3 + 8t, y = 15t, z…

A: Solving only ques 1 according to guidelines.

Q: Let C be the line segment connecting the points P(−2,1,−4) and Q(5,−4,3). Evaluate ∫C(2x+4z)dy…

A:

Q: Let l1 : (x, y, z) = (131, 89, −83) + r (42, 28, −28) where r ∈ R and l2 : (x, y, z) = (29, 21,…

A: LetandShow that the lines  and  are identical.

Q: Let a and b be real numbers. Let L be the line defined as L: æ = 6 – 6t, y = -11+t, z=a + bt, te R…

A: Suppose P : Ax+By+Cz=D is a plane and L: x-x0a=y-y0b=z-z0c=t is a line .If L is parallel to D then…

Q: Let L be the line defined as L: r = 5 – 5t, y = -9 + t, z= a + bt, teR Let D be the plane defined as…

A:

Q: uppose that L is parallel to D. The distance between L and D is V90.

A: b=59 a=114

Q: 1) Evaluate the triple integral. | 6xy dV where E lies under the plane z = 1+x + y and above the…

A:

Q: iven the points A(2,6,0) and B(3,5,6) determine the point of intersection of this line to x-z plane.

A: Given points are A(2,6,0) and B(3,5,6) The line joining points (x1, y1, z1) and (x2, y2, z2) have…

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

A:

Q: Let a and b be real numbers. Let L be the line defined as L: 3- 3t, y =-5+ t, z= a+ bt, teR Let D be…

A: Given :- parametric equation of a line L and equation of a plane D are given. Also L and D are…

Q: In the diagram, A is located at (0, 0), G is located at (5, 4), and I is located at (8, 4). Find the…

A: Given points: A is (0,0) G is (5,4) I is (8,4) Let the length of AC be 2a. Therefore, AF = CF = a…

Q: K Let R be the region bounded by the following curves. Use the shell method to find the volume of…

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Q: Identify the interval on which the series is valid.

A:

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.