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 = (-4,0) to the line through the points A = (-5,0) and B = (2,3) is 3

Q: Find k so that the line through (4, -1) and (k, 2) is a. parallel to 2x + 3y = 6, b. perpendicular…

A: The line passes through the points (4, -1) and (k, 2). Then the slope (m) of this line is: m = [2 -…

Q: Calculate the distance from the point P(9,4,3) to the line which contains points A(1,0,1) and…

A: we use  product rule to find distance between line and point

Q: Show that the lines determined byr 1(t) = < 7, 3 − 4t, 2 + 6t> andr 2(t) = <6 − t, 3 + 8t,…

A: Given: r1(t)=7,3-4t,2+6t r2(t)=6-t,3+8t,9-5t For r1. x-7=y-3-4=z-26=t For r2. x-6-1=y-38=z-9-5=t…

Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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Q: Find r so that the line through (2,6) and (-4,r) a).parallel to 2x-3y=4 b). Pendicular to x+2y=1

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Q: Which of the following lines passes through the point (3, –7) and is perpendicular to the line whose…

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Q: If the direction vector of a line is 3i + 2j and the gradient of another line is −5/2, find the…

A: Given, direction vector of a line is 3i + 2j, gradient of another line is -52, we have to find acute…

Q: Find the symmetric equation of line L, that passes through the points (1, 8, 9) and (5, 9, 0).…

A: 9

Q: 2. Find an equation of the plane parallel to the line

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Q: Find the equation of the plane passing through (0,0,-4)and perpendicular to the line joining the…

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Q: Find the equation of a plane bisecting the line segment joining (2,0,6) and (6,2,4) and…

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Q: Find the distance from the point A(2,4,3) to the plane determined by the three points B(1,4,2),…

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Q: Determine the equation of the plane that passes through (2,-4,1) and is perpendicular to the line of…

A: A plane is passing through 2, -4,1 and perpendicular to the line of intersection of the plane  3x -…

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

Q: Find the equation of the line that contains the point (1,–1, 2) and is perpendicular to the plane 2x…

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

A: The direction vector of the line  given by:        x=1+4ty=2+1tz=3+3t is :    r→=123+t413 So, The…

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

A: Answer

Q: If the line through the point (3.-4,-1) and parallel to the vector i+j+k. The equation of the line…

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Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

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Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

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Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

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Q: A yacht is travelling on a course parallel to and 80 kilometers from the straight shoreline of…

A: Given,         A yacht is traveling on a course parallel to and 80 kilometers from the straight…

Q: If Point S' is located at (-1, 4) which axis was IS -5 -4 -3 -2 1-1 1 2 4 5 6 -2 5. 2. 1.

A: Given that  the point (-1,4)  is located in co ordinate axis

Q: The points P, Q and R have coordinates (8, 7), (−2,−1) and (−6, 5) respectively. Show that the…

A: The point P is (8,7) and find the equation of the line passing through the point (8,7).The line…

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: Find an equation of the plane containing the point P(1, -2, -2) perpendicular to the line through…

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Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: Find the equation of the plane containing the point (7,-2,-5) and is perpendicular to the line…

A: We have to find the equation of the plane

Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

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Q: Let L, be the line passing through the point P1=(-1, -2, -2) with direction vector d-[-3, -3, 1]",…

A: L1 is the line passing through the point P1(-1 , -2, -2) with direction vectord→ = -3, -3, 1Tand L2…

Q: The symmetric equations for the line passing through (-3,–4, -5) and parallel to the vector (1,7,–…

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Q: Find equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

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Q: Find the DC’s of the line that is perpendicular to each of the two lines whose directions are and

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Q: Find the equation of the plane for all points equidistant to (1, -1, 1) and (0, -5, -2).

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Q: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: Find an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

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Q: Q2 / A man moved from the point (2, -2, 1) to the point (8, 3, 4). Express the displacement moved by…

A: The given point is                    P1 (2, -2, 1)  and  P2 (8, 3, 4) To find displacement in terms…

Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: Find the distance from the point P(-1,3,-5) to the plane through the three points Q(3, 1, -3). R(4,…

A: The points passing through the plane are: Q3, 1, -3R4, 6, -5S5, -4, -6

Q: standard form of the line with center (5,1) and tangent to the line 7x+2y=17

A: Given Data: Center: (x1, y1) = (5, 1) Tangent: 7x+2y=17   The general equation of tangent is,…

Q: Find the equation of the plane passing throught (0,0,-4) and perpendicular to the line joining the…

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Q: Find an equation for the plane containing the two (parallel) lines v, = (0, 1, –4) + t(1, 3, –5) and…

A: Solution: The objective is to find an equation for the plane containing the two parallel lines

Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

A: