The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. So the distance from P = (2, –4, –1) to the line through the points A = (-2, –3, –3) and B = (3,0, -5) is

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

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Q: The distance d of a point P to the line through points A and Bis the length of the component of AP…

A: Formula used: The equation of line passing through the point x1,y1  and (x2,y2) is…

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: Given: Points.P=(0,4,-1)A=(4,3,4)B=(-2,2,1)

Q: Find symmetric equations for the line through (1, 3, -2) and perpendicular to both u and v, where u…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: The given points are,

Q: For what values of z and y is orthogonal to both (-1 and

A: Remark: We know that two vectors are orthogonal if they are perpendicular to each other. i.e., the…

Q: – 2x + 4y -dA, where R is the parallelogram enclosed by the lines 5y Find - r - R - 2x + 4y = 0, –…

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Q: Find a general form of an equation of the line through the point A that satisfies the given…

A: Consider the given line 3x+2y=7. To find the equation of the line perpendicular to the given line…

Q: The distance d of a point P to the line through points A and B is the length of the components of AP…

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Q: Find a general form of an equation of the line through the point A that satisfies the given…

A: Our Aim is to find the general form of an equation of the line passingthrough the point A(7,-3)…

Q: -(39) is the value of a so that the line r 2 – 3t, y = 1 + at, z = -3 + 9t is z +5 x + 1 y + 2…

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Q: 20. Find the equation of the line through (13, 5) which makes an angle of 45 degrees with the line…

A: Given point is 13,5 and angle is 45°given equation is 2x+3y=12find the equation of line

Q: When the axes are rotated through an angle 4 π , find the transformed equation of 3x2 + 10xy + 3y2 =…

A: Axes are rotated through an angle 4π given equation is                             3x2+10xy+3y2=9…

Q: Given plane z: 3x+2y+=-3=0, point P(1, -2, 3), and lines 1₁:¹¹ and 4₂: (3, 6,-5)+r(2, 3, 1), find:…

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Q: (1.) (a) Find the intersection point of the lines ri(t) = (3, 2,0) + t(2, -2, 2) and ra(t) = (5,0,…

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Q: 9. Write an equation of the plane that passes through (2,0, –3) and (a) is perpendicular to the line…

A: Given: The vectors are: a=-1, -2, 3b=3, 0, -2v=2, -5, -4 The equation of plane is, P=2x+y=z+13

Q: Given the lines l and l2; l : x = 1+t, y = -2 - t, z = 3- 2t, y+1 3- z 3 i. Show that and are…

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

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Q: 1. Find an equation of the perpendicular bisector of the segment joining(3. -1) and (-1. 7). (A) x +…

A: Here we have to find the equation of line which is perpendicular bisector of the segment joining(3.…

Q: A circle C passes through (1, 1) and cuts the following two circles orthogonally: S, :x +y-8x-2y+16…

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Q: Draw a plane perpendicular to the horizontal plane inclined to the vertical (vertical) plane at an…

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A:

Q: The distance dd of a point P to the line through points A and B is the length of the component of AP…

A: Given,           The distance d of a point P to the line through points A and B is the length of the…

Q: Find the parametric and symmetric equations for the lines with the following conditions. (a) Passing…

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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 lį be the line described by the Cartesian equations • x = 1 • y-5 = 2(z-4) Let l2 be the line…

A: To find the distance between two lines we need to find general point on the two lines and then the…

Q: 4. In the xy-plane, the line.determined by the points (3, a) and (a, 12) passes through the origin.…

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Q: Q.10 If a 2i-3j + 4k and b-2j +4k Find the component or projection of a along b.

A: Component or projection of a→ along b→ is  a →. b→b→.

Q: 18. The diagonals of parallelogram ABCD intersect at E. If DE = 4y + 1 and EB = 5y- 1, find y, DE…

A: Given ABCD is a parallelogram.The diagonals intersect at E. DE=4y+1 and EB=5y-1

Q: Given the points A(3,5) and B( – 3, – 7), find d. the scalar equation of the line.

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Q: Given the lines 1₁ and 12; l₁ x = 1 + 3t, y = 26t, z = 7t - 3, 1₂: x=4=6-y=5—2 -8 3 5 (a) Show that…

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: Solution:-

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The distance d of a point P to the line through points 4 and B is the length of the component of P…

A: If a vector passes through the points Cx1, y1 and Dx2, y2, then its position vector is defined as…

Q: 5. Find the coordinates of the point P(2,4) with respect to the translated axis with origin at…

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

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Q: Given the point P (2, 4, –1) and the line L: x = 1+ t; y=2+ 4t ; = =-3t Find the equation of the…

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: Consider the provided information, Given P=2,-4,A=5,-1 and B=-3,-5. We know that the formula for the…

Q: when the axes are rotated through an angle x/4,find the transformed equation of 3x2+10xy+3y2=9

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Q: When the axes are rotated through an angle x/4,Find the transformed equation of 3x2+10xy+3y2=9

A:

Q: 19. Find the angle between the line and the plane of the following equations, a. 4:r= 2i +3j-k+(2į -…

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Q: Which of the following is an equation for the line through the point (2, 3) and perpendiçular to the…

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Q: In each case, determine whether or not the lines have a single point of intersection. If they do,…

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Q: 4-Sy. dA, where R is the parallelogram enclosed by the lines x- Sy - 0, x- Sy 9, 4x-y 1, and x- y=7…

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A:

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: Distance from line in 3D

Q: 19. Find the angle between the line and the plane of the following equations, X_ y- 2_ 3z+ 3 b. L:…

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Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

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.