O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

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Q: 6. Find the shortest distance from B6,0,0) to the pane Ax + By tCz +D= 0 where A, B,C and D SR .

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Q: What is the shortest distance from the curve x^2+xy+y^2=16 to the origin?

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Q: a bounded by the curve y = 3VI and the lines z = 6 and z= 8 above the z – azis is Võ+ 12v6 O 10

A: We have to choose the correct answer

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: Find the equation of the tangent line to the given curved as directed. x²+2y=8 perpendicular to the…

A: topic - equation of tangent line

Q: Consider the path r(t) = (4t,2t 2 ,2lnt) defined for t > 0. Find the length of the curve between the…

A: Given the path r(t) = (4t, 2t2, 2ln t), t>0. Find the length of the curve (4, 2, 0) and (20, 50,…

Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

A:

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 shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: T Find the tangeut line to the curve 1 2rg+ 12 at the point (2. 1).

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Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

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Q: Find the distance from the point S(1, 1, 5) to the line L: x = 1 + t, y = 3 – t, z = 2t.

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Q: Sc 7ydx + 3z dy where C is the straight line path from (2, 4) to (4, 7).

A: The parametric equation of the straight line between the points (a,b), (c,d) is x-ac-a=y-bd-b=t,…

Q: y = 4 1 ,2 In x, 1<x < 2 2 -

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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: A. Find the shortest distance between the point A (3, 10) and the line y=x+1.

A:

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: compute the length of the curve over the given interval. r(t) = 2ti − 3tk, 11 ≤ t ≤ 15

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Q: Q6) 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: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

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Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

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 the length of the curve defined by from = 9 to z = 10. 2 y-4lm (()²-1) =

A: find derivative

Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

A:

Q: A. Find the shortest distance between the point A (3, 10) and the line y = x +1.

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Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

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: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

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Q: Find the length of the curve given by r(t) = for -5 <t<5. O 5/19 O 10/10 O 10/19 O 5/10 O 10

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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: Find the per pendicualar olistace from the P (5,6) to the line -2xr+3Y+4=0.

A: Formula for perpendicular distance is as below : Given :-2x+3y+4=0Ax+By+C=0A=-2B=3C=4 Point  (m , n…

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

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Q: 4. Find the are length of the curve from y=1 to y-4

A: The given curve is x=18y4+14y-2 from y=1 to y=4

Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

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Q: (1) ( ) Find the shortest distance between two lines given x +2 -8 y = and y 2

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Q: Find a distance from the point S(1,1,5) to the line x=1+t, y=3-t,and z= 2t

A: We need to find the distance of the point (1,1,5) and the given line.

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: Question 15 Find the distance from S= (1,1,5) to the line L: x=1-1, y=2-t, z=31.

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Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

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Q: 3. Find the length of the curve y = x - In a, 1< x < 4.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

A: