Let P(-4, 1, -3) be a point that is not on the line L . Let the line L pass-through points Q and R and be defined parametrically: x=-3+t, y+4-4t, z=2t The shortest distance, d, from point P to the line L is d= |a * b | / |a| . Use this formula to find the distance from point P to the line L .

Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: Find the point on the line x /a + y/ b = 1 that is closest to the origin.

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Q: Let P(x1, y1) and Q(x2, y2) be two points in the plane. Prove that the equation of the line through…

A:

Q: Plot the points A = ( - 1, 8) and M = (2, 3) in the xy-plane. If M is the midpoint of a line segment…

A: We have the following information    We have to plot the points A = ( - 1, 8) and M = (2, 3) in…

Q: a) Find the distance between the point P (9, 1) and the line 3x+4y 6.

A: As per our guidelines we are supposed to solve only one question i.e. the question no (a). For the…

Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

Q: a) Find the distance between the point P=(9, 1) and the line 3x+4y=6.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the distance between the point (-3, 1, 5) and the line given by x = 5+t, y = 1- 2t, and z = 3-…

A: Given : Point A ( -3,1,5) x = 5+t  y=1-2t  z=3-t

Q: Consider the line which passes through the point P(5, 5, -5), and which is parallel to the line x =…

A: Equation of the line :       x-x0a = y-y0b = z-z0c=k ; where x0,y0,z0 is a point and a,b,c is the…

Q: Let l be the line given parametrically by x = (1, 3) + t(-2, 1), tЄR. Which of the following points…

A: A parametric equation is an equation that employs an independent variable  to define the dependent…

Q: Find the distance of the point (3, 2, –4) from the line r(t) = (1+ 3t, –1+ 2t, 3 – 3t).

A: for finding distance of the point3,2,-4 from line rt=1+3t, -1+2t, 3-3t we assume a point1+3t, -1+2t,…

Q: Find the distance from the point P(2,1) to the line y = x + 2 *

A: Given point is P(2,1) and the line is given as y=x+2 1x-1y+2=0 The formula to find the distance…

Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Determine the distance between: the pa rallel line x-a++ X - 3+S+t t9= 5-t,tER and the…

A: Given line is                                                     x=2+ty=5-tz=-4 point on the line…

Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

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Q: Let A be the point with coordinates (-3, 2, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Let Q(0,-1,1) be a point in space and let u have the line L whose equation is L: 3- 3x = 1 – 3 y…

A:

Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

A:

Q: Show that the following sets of points are collinear and find the equation of the line L containing…

A:

Q: Show that the following sets of points are collinear and find the equation of the line L containing…

A: \

Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: Let M be the midpoint of a line segment joining two points P(8, -2) and Q (6, 10). Calculate the…

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Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: Let I, be the line described by the Cartesian equations • x= 1 • y-9 = 2(z-7) Let l, be the line…

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Q: Use the result in Exercise 21 to find the equation of the line that contains (5, – 1) and is…

A:

Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: . Find the relation between line L and plane P: Question 9. 2x +2y-32-1=0. If they intersect at one…

A: The given plane is 2x+2y-3z-1=0. Find the relation between line L and plane P. 1. The given line is…

Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

A:

Q: Given the function f 1x2 = 1 - cos x and the points A1p>2, f 1p>222, B1p>2 + 0.05, f…

A:

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: Find the length of the following three-dimensional curve. r(t) = (2+5t,9-3t, -6+3t), for 1st≤4

A:

Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.

Q: The distance from a point P₁(x1, y₁) to the line ax + by + c = 0 is lax₁ + by₁ + cl √² + b² Use this…

A: SOLUTION-

Q: Given two lines L1 : x =t+1, y = 3t + 1, z = 2t – 1, and L2 : x = 2t – 2, y = 2t + 3, z =t +1,…

A: The given lines are L1:x=t+1,y=3t+1,z=2t-1L2:x=2t-2, y=2t+3, z=t+1 and a plane H is parallel to both…

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

A:

Q: Which of the following mathematical models is used to determine the distance between two points…

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Q: Show that the following sets of points are collinear and find the equation of the line L containing…

A:

Q: In a certain geometry, define the distance d(P₁, P₂) between two points P(x, y,) and P(x, y₂) as…

A: We will use the basic knowledge of metric spaces to answer this question completely and correctly.

Q: find the distance from the point to the line (2, 2, 0); x = -t, y = t, z = -1 + t

A: Given information: The point to the line is (2, 2, 0) and x = -t, y = t, z = -1 + t. Calculation:…

Q: Find the point on the line x + 2y = 5 that is closest to the origin.

A: Let the point (x, y) on the given line x+2y=5  is closest to the origin (0, 0). observe that…

Q: Let A be the point with coordinates (0, -3, 3) and let B be the point with coordinates (2, 0, 0).…

A: Given: A=0,-3,3B=2,0,0

Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

A:

Q: Let L, = x - 5y + 10 = 0, L, = 4x + y – 1 = 0 be two lines. 1. Show that the lines L, and L2 are not…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l.

A: In a 3 dimensional space, a point and a line can be at infinite number of distance from each other,…

Q: Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written…

A: We have to show that the equation of the line in R2 through distinct points x1,y1 and x2,y2 can be…

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.