2. Let l be the line with equation x = 2y = z +3 and let P be the point (1, 1, 1). Consider a line through P which intersects l in a right angle. Find the coordinates of the point of intersection, showing working.

Q: (1) What is the relationship etween lines 11 and 12? where L:x = 2, y = 1+ 2t, z = 1+t L2:x = 4 -t,…

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Q: Let l,,l2,lz be the lines X(t) = (1,1, 2) + t(1,2,3), X(s)= (9,8,11) + s(2,1,1) and X (r) = (0,0,0)…

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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. distance

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Q: 3) Let M be the midpoint of a line segment joining two points A(20, -1) and B (4, –9). Calculate the…

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Q: Find a line that is parallel to the line that passes through both P and Q and contains R.

A: We have to find the equation of line.   According to our guidelines we can solve only one question…

Q: Let line L: x = 2t, y = 0, z = 3, and let line M: x = 0, y = 8 + s, z = 7+s, for some constants t…

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Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

A: Answer

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 to the given line x 1+t, y= 3-2 2t, z=4- 3t and point (4,1,-2)

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Q: 3. Show that the lines L1 : x = 2+t, y= 2+3t, z = 3+t and L2:1 = 2+t, y= 3+ 4t, z = 4 + 2t…

A: L1: x =2+t , y= 2+3t , z= 3+t  L2: x =2+t , y= 3+4t , z= 3+t

Q: Evaluate ∫C x ds, where C is the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).

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Q: Show that these two lines are coincident. L1: [x, y, z ] = [1, 5, − 2] + s [1, 7, − 3] L2: [x, y, z…

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Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

Q: Find the distance from the point (1, 2, 0) to the line æ = 3t, y= 1, z= 2 – t.

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Q: Construct a line perpendicular to the line given through the point P at the right.

A: To plot the line perpendicular to the given line through the point P

Q: 4:x=1+21, y =-2+t, z=4-t 1, :x = 5–3s, y= 4- z = 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: Find the distance of the point (2, 2, –5) from the line r(t) = (1+4t, –1+ 4t,7 – 3t) %3D swer:

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Q: 15. Find the angle between the straight lines I, and l, which are defined by x-2 y+1 =1-z. 4:x=1+2t,…

A: The angle is, 85.75°  The detailed solution is as follows below:

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. %3D

A: Given line is                                                       l:1, -1, 1+t0, 2, 1 vector…

Q: 3. The line L is parallel to the line x t, y 2t, z =3 and passing through the origin.

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

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Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

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

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Q: Find the distance from the point S= (1, 2, 1) to the line x = 2-t, y=-1+2t, and z=2+ 2t.

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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: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: 3. Show that the lines L :1 = 2+t, y = 2+3t, 2 = 3+t and La :1 = 2+t, y = 3+ 4t, 2 = 4+ 2t…

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Q: Find the distance from the point to the given line x =1+t, y= 3-2 2t, z=4- 3t and point (4,1,-2)

A: To find  The distance from the point to the given line.

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

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Q: 1. (x² +y² +z?) ds , where Cis straight line from (1,2,3) to (4,1,4).

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Q: Find the point ( x, y) such that (1, 3) is the midpoint of the line segment connecting а. (х, у) and…

A: NOTE-Since you have posted a question with multiple sub-parts, we will solve first three subparts…

Q: Find x'z ds, where C is the line segment from (0,2,-3) to (6,0,-6) C

A: To find:∫Cx2z dsThe line segment is from 0, 2, -3 to 6, 0, -6

Q: Find the distance from the point (1, 5, 5) to the line x = 0, y = 5 + t, z = 5 + 5t.

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Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: We are given two lines L1 and L2 in 3d, and we have to find the closest points x1 , x2 such that the…

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: C. Show that the lines with symmetric equations (x y z) and (x+1 are skew, and find the distance…

A: L1 ;  x=y=z     x-01 =y-01=z-01  x1=0    y1=0     z1=0α1=1    β1=1      γ1=1L2:  x+1=y2=z3…

Q: 4) Evaluate , -dz, where y is the line from 1 → 1+ i

A: In complex integration, we have to convert our given question into complex terms. But in our…

Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

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: Y Find S Zdz Such that c is the line which joining A,B,C and D as follows A (o,1) yB (2,1) , C…

A: Here, firstly we have draw the line C with the given points. Then we have to find integration value…

Q: Find the line through (1,-1,1)and normal to the line  3x=2y=z , and parallel to the plance  x+y-z=0…

A: Equation of the line: The equation of a line passing through the point (x0, y0, z0) is given by (x,…

Q: Construct perpendicular lines from point P to line m. 1. VE

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the point of intersection of the lines r;(t) = (-1, 1) + t(8, 4) and rɔ(s) = (2, 1) + s(8, 6)…

A: Consider the given lines in polar form. To find the intersection points equate the x and y…

Q: If the point (4, 1) is the midpoint of the line PD , where P (x, 3),  D (7, y)   ,  find the value…

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Q: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

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Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. *

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Q: Explain why the lines below intersect. l1: (x, y, z) = (2, 3, 4) + n(1, 2, – 3) and l2: (x, y, z) =…

A: Given : Vector equation of the line l1 : x, y, z=2, 3, 4+n1, 2, -3 Vector equation of the line l2 :…

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: Evaluate ydx + yedy + (y + 2)dz where C is the line segment from (1, 1, 3) to (4, 4, 6).

A: We find the integration of given function.

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.