Q.2 Let line (L): x = 2t, y = 2 + 5t , z = 3 + 2t if (a,1,b) lies on line .Find (2a + b)? point

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: B. Show that line is parallel to plane x-2y + z 6

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Q: 04: Find the distance between the parllel lines L, and L2 where L1: x = 2 - t, y = 2t, z = 1+t L2: x…

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Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

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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 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: the distance between the two skew lines L and L2. L: x=3+3t, y=-1-4t, z=4+2t. L2: x=6+5p, y=3-p,…

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Q: 3) Determine the point of intersection between Line L: ( (x+1)/6)= ( (3-y)/-1)= ((z-4)/-2) and i…

A: Given, Equation of line is x+16=3-y-1=z-4-2.Equation of plane is x+2y-z+29=0. The intersection point…

Q: Determine B such that the line 3x +2y – 7 = 0 is perpendicular to 2х- Ву+2%3D0. O A. 5 О В.4 С. 3 O…

A: Let m1 and m2  be the slopes of the lines L1 and L 2 . If  L1 is perpendicular to L 2  then m1×m2 =…

Q: 2. Evaluate . 3x – 6y ds for C is the line segment from (6,0) to (6,6).

A: Let C be a piecewise smooth curve defined by, Let P and Q be two continuous functions of x and y…

Q: Evaluate (x+y)ds where C is the straight-line segment x = 2t, y = (8 – 2t), z = 0 from (0,8 C…

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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: B. Find the distance between the point (1. 1.3) and the line =z-3) OMI NOTL

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Q: 2) Determine whether the lines 1: x = 1+ 2t, y = 3t, z = 2 – t and l2 : x = -1+ s, y = 4 + s, z…

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Q: ind a plane containing the point Gl,2,-3) and the line of intersection of the pladnes -X+3y -Z E -7…

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Q: Let C be the line segment connecting the points P(−2,1,−4) and Q(5,−4,3). Evaluate ∫C(2x+4z)dy…

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Q: 4. Determine the intersection of lines:L = aund LzX= とz 11 >\J

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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: O which line lo pavallel to HiS line: y=-Zx-7 A. Zメとらyこう B.2x-54こ50 3D4 D. SX

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Q: Consider line segment PQ on the coordinate plane. Exit Ticket-4/30/21 Ifa student translates line…

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Q: 4. Determine whether the pair lines are equal, parallel but not equal, skew, or intersecting. L1:x =…

A: Given:      L1:  x=1-4s, y=3+s ,z=8-6s      L2: x=2+3t ,y=2t ,z=-1-3t   For Parallel test:…

Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

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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: 7. Reflect parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,–4) in the line y = -x.…

A: Reflection in Y axis  : (x , y ) → (-x , - y )

Q: 9. Are the lines parallel, perpendicular or neither. Show work. 4. y3-x+2 3 3x+4y = 4 %3D

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Q: Show that -ydx+xdy) = x₁y₂-₂₁ where C is the line segment joining (x,y) and (x₂,₂).

A: We have to prove ∫C-ydx+xdy=x1y2-x2y1 Where C is the line segment joining x1,y1 and x2,y2 Now…

Q: 4. Determine whether the pair lines are equal, parallel but not equal, skew, or intersecting. Lị:x =…

A: Recall: Given two lines  L1:  x1=a1+b1s  , y1=c1+d1s   , z1= e1+f1s  L2:  x2= a2+b2t  , y2=c2+d2t…

Q: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

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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: 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: Show that the two lines X= 2+ St J= 4 - 36 Z: 5+t X= 1+4t and y= 5-4t Z: -1+ SE skew Rind the…

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Q: The equation of a line perpendicular to 4x+7y– 63 =0 is Oy- z 6 Oy--- I. Oy =z+

A: See the details solution in below

Q: 10. In the standard (x, y) coordinate plane, line r contains the points (6, 5) and (b,-5), and line…

A: Given problem is :

Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: ind an equation of the line of intersection of the following two plane x + y + z = 0 nd 2я — у + 32…

A: We have to find out

Q: 5. Find the point of intersection of the following lines x = 4t +2, y = 3, z = -t +2 b. x = 2s +6, y…

A: Given query is to find the point of intersection of line a and line b.

Q: Show that the two lines X= 1+4t X = 2 + St and y= 5-4t J= 4 - 36 Z: -1+ SE 2: 5+t Rind the distance…

A: There are two equations of line:

Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Show that the lines with symmetric equations L1 : = = and L2 : 팡!%3D 부 =D 촬 %3D y-3 are skew.

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Q: Find Sc((x² + 3y)i + 3y³j) · dr' where C consists of the three line segments from (2, 0, 0) to (2,…

A: Given ∫x2+3yi→+3y3j→.dr→ where C consists of the three segments from (2,0,0) to (2,2,0) to (0,2,0)…

Q: , in general form (x + y2 + Bx + Cy + D = 0), centered a he lines 2x + y + 10 = 0 and x - 2y - 5 = 0…

A: We have to find the equation of a circle whose center is the point of intersection of,  2x+y+10=0…

Q: 2. Find the area of the triangle formed by the lines Sz + y – 14 = 0, z + 7y + 38 = 0, and 9z – 5y +…

A: First we find vertex of triangle by using given lines.

Q: 1. LORS and ZSRQ are a linear pair. If M2ORS = MLSRQ = 3x- 6, find x. %3D %3D S R Q

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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.