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

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: A line passing through (0, –3) and is perpendicular to y =;x – 4. х —

A: The given line passing through the point 0,-3 and it perpendicular to the line y=52x-4. Calculation:…

Q: . Calculate the area of the triangle formed by the line 3x-7y+4 =0 , and the (ans.: 8/21) axes.

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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Q: Find the shortest distance between the lines i-(i+2j+k) + 2(i-j+â)and 7= 2i - j-k + 4(2i + j+ 2k)

A: The equation of the given lines are r→=i^+2j^+k^+λi^-j^+k^r→=2i^-j^-k^+μ2i^+j^+2k^ It is known that…

Q: 5. The ends of the transverse axis are at (+8,0) and the ends of the conjugate axis are at (0. 16).

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Q: Find the equation of the plane through P(4, 3, 6) and perpendicular to the line joining P(4, 3, 6)…

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

A: 9

Q: 8) Determine an equation of a line that passes through the point P (5,-2,3) and is parallel to the…

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Q: The line in R that is parallel to the y-axis and passes through the point (1, 2, 3) has equation + t…

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Q: #3 Find the line equation(s) of the line(s) through point P(1, 0, 1) that meets the following line…

A: Given :  Given:P(1,0,1)L: x,y,x=1,2,0+t2,-1,2P0=1,2,0Aim: To find a line(s) through point P,…

Q: 6. Find an equation of the plane through point P(2, -4, 2) that contains the line F(t) = (2+ 3t, t,…

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Q: 1. Find the line L passes through the point (1,2) and parallel the line L': x + 2y = 3.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: In the xy-plane, how many points on the curve y² + x² = 3 – xy have horizontal or vertical tangent…

A: The given curve is  y2+x2=3-xy

Q: Find an equation of the line L that passes through the point  (−2, 6) and satisfies the given…

A: Given,            The line L that passes through the point (−2, 6).Since, L is perpendicular to 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: Find the equ. nf line through the Pont (-2,3,4) and Parallel to Planes: 2X+3y +42=5 3X + 4Y+52=6…

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Q: Find the shortest distance between the skewed lines. l1: = 1+ 2t, y = -1+t, z = 2+ 4t and l2: x= -2+…

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Q: Find the equation of the plane with the given description. Passes through P = (3, 5, −9) and is…

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Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

A: Given points are: 4,-1 and -2,3 The distance between the points 4,-1 and x,y is: d1=x-42+y+12 The…

Q: The plane that passes through  (9, 0, −3)  and contains the line  x = 6 − 3t, y = 2 + 5t, z = 4 +…

A: Given : A point (9,0,-3) where the plane passes through.             A system of equations for line…

Q: In Problem,find the distance from P1 to P2.

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Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

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Q: Find K so that the line through( 1, 5 )and( K, 8) is a) parallel to 4y -3X =7 and b) perpendicular…

A: compute the equation of a line joining (1,5) and (k,8) by using below formula.

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: 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 the relationship between x and y such that point (x,y) is equidistant from the points (7,1) and…

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Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: We know that the equation of a line passing through the point a and parallel to the vector b is…

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

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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 an equation of the plane through (1,3,–2) and the line of intersection of the two planes with…

A: Given that, Point A (1,3,-2) Two planes  P1: x-y+z-1=0P2: x+y-x-1=0   We have to find the equation…

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 a relationship between x and y such that (x, y) is equidistant (the same distance) from the two…

A: If the distance from (x,y) to the points (3,2) & (5,-1) are equal, then the squared distance is…

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

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Q: Let A(x,y) be the point on the line y = x + 1 that is closest to the point B(2,0). Then the square…

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Q: Find k so that the line through (4,4) and (k,6) is a) parallel to 5y- 2x = 73; b) perpendicular to…

A: Solution

Q: Find k so that the line through (3, 2) and (k, 3) is a. parallel to 25x + 17y = 34, b. perpendicular…

A: We will be using the following concepts: Parallel lines have the same slope. The product of slope…

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: 2. Find the equation of the line that is parallel to the intersection of planes 12, 2x-8y + z = 0…

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Q: Find an equation for line that passes through point p(8,6) and perpendicular to v=2i+3j

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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: Find the z-coordinate of the foot of the perpendicular from A(1, 1, 1) on the line joining B(1, 4,…

A: We will solve the problem.

Q: Find the value of k such that the perpendicular distance of the point (2,k) from the line x - 2y =…

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Q: Find an equation of the plane through the three points given: P=(0,0,3), Q=(2,−3,2), R=(−1,1,0)

A: find the equation of the plane