Find the point o

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 the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

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Q: Find the point at which the line intersects the given plane.

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Q: Which of the following is the equation of a plane parallel to the cz-coordinate plane and passing…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Ex(29):- Determine whether the line and the plane are intersect; if so, find the point of the…

A: Given, The equation of the line   L : x=t, y = t, z =t  Equation of the Plane : PL : 3x-2y+z-5=0…

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

A: We have to find the point where the line x=83+2t, y=-2t, z=1+t intersects the plane 3x+2y+6z=6.

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 an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

Q: Find the point of intersection, if any, of the plane T: 4x + 2y – 2z=1 and the line l : 3 +t 1

A: Point of intersection of line and plane

Q: O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

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Q: draw the plane given by the equation  x + y + z = 0

A: x+y+z=0 It is a plane passing through origin.

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: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

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Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1 and…

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Q: Determine whether the plane x + y + z = 9 and the line x = t, y = -2t + 1, z = t + 2 are parallel,…

A: The given equation of line is in parametric form, x=ty=-2tz=t+2 Convert it into the cartesian form,…

Q: To which coordinate plane is the plane y = 1 parallel?

A: y=1

Q: Draw the plane given by the equation. x + y + z = 4

A: x+ y+ z= 4

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Find the x-, Y-, and z-intercepts of the plane. (If an answer does not exist, enter DNE.) 2x + 3y +…

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

A: Given that:                    The line with equation:      x=83+2t, y=-2t, z=1+t     & Plane:…

Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

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: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: Find the cartesian equation of the plane determined by the two intersecting lines x-4 y+1 z-2 L1: 3…

A: Here,  v1=3i+2j+kv2=5i+3j+2k v1×v2=ijk321532=i4-3-j6-5+k9-10=i-j-k Thus, the equation of the plane…

Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Given:   Plane→   2x+3y = 10  Line→       x-1 3= y+1-2 = z-9

Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

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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: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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Q: Find the equation of the line of intersection of the following two planes: Plane A: 2r – 3y + 2z =…

A: Given Plane A : 2x - 3y + 2z = 5Plane B : x + 2y - z = 4To find the intersection point, Put z = 0 ,…

Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

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Q: Let u = 2 and v = | 0 , and let P = span{u, v}. Find an equation for the plane P.

A: Given: Let xyz be a point in Span {u, v} so there are t, r∈ℝ such that xyz=tu+rv. So,…

Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: Find the equation of the plane containing the following two lines: L1 : te R 1 L2 : +s. seR 1

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Q: Find the intersection of the following geometric objects: the plane 3x - y + z = 3 and the plane 2x…

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Q: Consider the plane P with equation x+2y+2z=-7 and line L with equations x=-4-2t y=4+7t z=-1+3t…

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Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

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Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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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.