Which point(s) lie on the line (x, y, z) = (2, – 1, 5) + n(1, 2, – 1)? a) (1, – 3, 4) b) (5, 5, 2)

Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

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 point at which the line f(z)= 5z + 21 intersects the line g(z) = - 2z -7 %3D -2 11 Submit…

A: To find the intersection point of the lines f(x)=5x+21 and g(x)=-2x-7.

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: Use calculus of variation to derive the shortest line (equation) that joining points (x,y,z) =…

A: Given plane -   7x + 2y + 3z = 7 Parametric equation will be =  (1 - t, 0- 2t, 0 - t) Hence,

Q: Evaluate (x+ y)ds where C is the straight-line segment x = t, y= (4- t), z=0 from (0,4,0) to…

A: Given that x=t,y=4-t,z=0 from (0,4,0) to (4,0,0) evaluate ∫cx+yds

Q: Which point(s) lie on the line (x, y, z) = (2, –1, 5) + n(1, 2, - 1)? a) (1,- 3, 4) %3D b) (5, 5, 2)

A: The given line is  (x,y,z)=(2,-1,5)+n(1,2,-1) compare  with general equation of line in a space

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: 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: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

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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: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

Q: Determine the way in which the line [x, y, z] = [2,−3, 0] + k[−1,3,−1] intersects the plane[x, y, z]…

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Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

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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, z…

A: we have to find the point of intersection of the given lines

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 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: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: Find the distance from the point P(2,1) to the line v = x + 2

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Q: d the eqation of the line that passes through A(1,2,1) and intersects the line x+1 у-2 z+1 %3D at…

A: Topic:- geometry

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: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. O (5)^0.5 O 7 O 2(3)^0.5 O…

A: Given: Equation of line is: X = 1+ t Y = 3 - t Z = 2t To find: distance from the point (1, 1, 5) to…

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 Polnt otintersectton of the lines: l,: x = 2+t, y =3+2t,z z 4 +3t X = S+ 2, y= 2S+4, 2=…

A: Here we will find the point of intersection of given lines,

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: Find the relationship between x and y such that the point (x,y) is equidistance from the points…

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Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

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 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: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: Find the distance between the skew lines i(t) = (3, 0, – 2)t + (7, 9, 0) and p(s) = (4, – 4, – 5)s +…

A: We have to find the distance between skew lines.

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: find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2

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Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: Find m, n ∈  R so that the line r X: (n, 2,0) + λ (2, m, m) is contained in a plane π: x -3y + z = 1

A: The direction cosines of the line, r(x)= (n, 2,0) + λ (2, m, m) are <2, m, m> . The direction…

Q: A normal equation of the plane that contains the line 1₁: (x, y, z) = (1, -1, 2) + t (9, 1, 3), t E…

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Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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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: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

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Q: Find the distance between two skew lines x = 5+t, y = 5 + 3t, z = 4 -t and x = 2t, y =t, z=t O 1 3 '…

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Q: Evaluate A dr where C is the line joining (0, 0, 0) and (2, 1, 1), given A= (2y + 3)I +xj+(yz – x)k.…

A: # given A=(2y+3)I+xzj+(yz-x)k  Then to find integral(A*dr) from (0,0,0)to(2,1,1)

Q: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

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Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: 2x + 3y Find -dA, where R is the parallelogram enclosed by the lines 4x – 4y -- 2x + 3y = 0, 2x + 3y…

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