Let l be the line (1,-1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. %3D distance = PQ + proj PQ PQ – proj, PQ PQ – projd PQ

Q: Let / be the line (1,-1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. perp PQ…

A: We have to find the perpendicular distance between point Q and line l. Point Q is 1, 0, 1 and line l…

Q: Find the distance from the point (3,4,1) to the line x=0, y= 4+2t, z= 1+t

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Q: Find the coordinates of the midpoint of the line segment PQ. P(x-Z, r), Q(x + z, r) Select one: O A.…

A: The mid-point formula of a line segment is, x,y=x1+x22,y1+y22 where x,y is mid-point of the line…

Q: Evaluate (x+ y)ds where C is the straight-line segment x = 3t, y = (12 - 3t), z = 0 from (0,12,0) to…

A: We need to evaluate the integral along the given line. First eliminate the parameter t.

Q: 3. In Etercises, verify that the given point is on the curve and find the lines that are latangent…

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

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: Find the distance between the lines: ri = +! r2 = + s

A: We have to find the distance between given 2 lines.

Q: Let l 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 the line equation l is 1,-1,1+t0,2,1 and the point is Q=1,0,1. Find the distance from Q to l.

Q: Find the EXACT distance (do NOT round) between these two lines. L1: [x, y, z] = [1, 3, 7] + t[–1,…

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

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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. %3D

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

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 distance from the point (1,1,5) to the line x=1+t, y= 3-t, z=2t O 2.236 O 0.36 O 36

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Q: Let P be a point not on the line L that passes through the points Q and R. The distance d from the…

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Q: Let M be the midpoint of a line segment joining two points P(8, -2) and Q (6, 10). Calculate the…

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Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1,√5). Find the coordinates of the point S on…

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Q: ) Find the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, z = 2+ t.

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Q: x = 5 +t, y = -1, z = 8+ 2t х — 2 у—2 2+1 3 -1 4

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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: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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

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Q: O Find the distance from the point (2, 1, 4) to the line r = (-t,6 – 2t, 8 – t).

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Q: Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

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Q: find the distance between the Linel L) through A(I,0,-1), B (-1,)andthe Line (L2) through C…

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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 the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, Z = 2 + t.

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Q: Evaluate |V(x? y + x y z?) . dr where C is the line segment from (1,- 1,0) to (2,1,3)

A: Dell Operator:The Dell∆Operator of a scalar function f(x,y,z)  is defined as   ∇f=∂f∂x i+∂f∂y j+∂f∂z…

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

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Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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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: Consider the line with equation OP + td where P = (1,1,0) and d = (-1,2,1). Notice that P is on the…

A: Given that the equation of the line in OP+td where P=(1,1,0),d=(-1,2,1) And given that Q=(1,2,-1)…

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: The distance between the two lines x = 1+ t,y = -2 + 3t, z = 4- tand x = 2s, y = s, z = s is a) 1/2…

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Q: Find the distance between lines x + 3y = 5 and x + 3y = 25.

A: The distance between two parallel lines can be calculated using the formula,

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: Consider the line with equation OP + td where P = (1,1,0) and d = (-1,2, 1). Notice that P is on the…

A: To find the projection: Find the vector from the point P and Q say a→ From the the given equation…

Q: Let 7 (t) = (3t2 – 1,t? – 2t3, Find the line (L) tangent to r(t) at the point (11, – 12, – 64) –…

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Q: Find the distance between the points (p, q) and (0,0)

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Q: Qre Show that The lines Z+3 w/ parals. are malle! 1-3. 3 %3D 9 3.

A: We know that for a line  By applying above formulae for given lines L1 : x-11=y+32=z+33 then…

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: 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) .

A:

Q: The distance between the two lines x = 1 + t,y = -2 + 3t, z = 4 – tand x = 2s, y = s, z = s is а)…

A: Consider the provided information, x=1+t, y=-2+3t and z=4-t And, x=2s, y=s and z=s Find the distance…

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: The vector form of the equation of a line L in R2 or R3 isx = p+tdwhere p is a specific point on L…

Q: 1. Find the distance between these lines L : [x, y, z] = [-2, 1, 1] + [3, 1, 1]; 1 € R L₂: [x, y,…

A: Distance between two lines

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.

Q: Let P be a point not on the line L that passes through the points Q and R. The distance d from the…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.