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)

Q: Find symmetric equations for the line through (1, 3, -2) and perpendicular to both u and v, where u…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: f (x, y) = x² + y² – 2x, D is the closed triangular region with vertices (2, 0), (0, 2), and (0, –2)

A: According to the given information, it is required to find the absolute maximum and minimum values…

Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

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Q: 24 dA - I 3x – Y when D is the parallelogram bounded by x – 2y = 0, x – 2y = 2, - and Зх — у 3D 1,…

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Q: Find the average value of f(x, y) over the plane region R.

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Q: Find the area of the triangle bounded by the lines y=x+3, y=2x-1 and y=-3x+4

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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 distance d between the point M(5, 2, 4) and the line x- 8 y -2 Z-2 %D -8 -9 7.

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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,…

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Q: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

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Q: Find the point of intersection of the lines: y = 4x + 1 and y = -2x +4 %3D o (2,9) 으(4,2) ㅇ (4,3) O…

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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: dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² =…

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Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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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: 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: 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: Find a plane containing the point (-3,-3,5) and the line x(t) y(t) z(t) = = 8 + 4t -4-6t -7-3t

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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: 3) Let r1(t) = and r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

A: Given r1(t)→=t,t+2,2t and r2(t)→=t+1,2t+1,t+1 are two skew lines. We have to find the equation of…

Q: dw dw Find ду and ду at the point (w, x, y, z) = (9,3,1,1) if w = x²y? + yz- z³ and x2+y² +z² = 11.

A: The solution of the problem is given in the next steps.

Q: Y = , cx. y) = (9,5) X-8 会? Jengent line -? at (9,5)

A: Explanation of the answer is as follows

Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: If D is the distance between the skew lines 4 x=1+t, y=1+6t, z=2t L2 x=1+2t, y=5+15t, z=-2+6t, then…

A: first we will  convert given parametric equations of lines, then we will find  a1,b1,a2,b2 after…

Q: 1)calculate xy dxdy D where D is a parallelogram with vertices (0,0) ,(5,-1).(3, 1) and (8,0)

A: We have to evaluate the integral ∬ xy dxdy over D where D is a parallelogram. First we will sketch…

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 a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: We know that the equation of a line passing through the point a and parallel to the vector b is…

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

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Q: 3) Let r1(t) = and_r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

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

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Q: Let z = 3x*y, find Vz.

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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: 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: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

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: Find the distance between the skew lines r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

A: Given r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

Q: Find the gereral Solution of the fille d dffferential equation. 3,n1 %3D | -

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Q: point

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Q: Find the values of ∂z/∂x and ∂z/∂y at the points z3 - xy + yz + y3 - 2 = 0, (1, 1, 1)

A: Given: z3-xy+yz+y3-2=0  At the points (1,1,1) To find: The values  of ∂z∂x and ∂z∂y.

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

A: To show that the given two lines are skew lines. The two lines are                          l1 = (-2…

Q: Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to…

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

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Q: Select all of the lines that go through the point (2, 5). Oy = (r- 5) + 2 O y = 2x + 1 %3D

A: We have given point (2, 5) a) OPTION (A) y=x-52+2 If the point (2, 5) lies on the above line then it…

Q: If p is the distance between the skew lines 4,:x=1+t, y=1+6t, z=2t Lz.x =1+2f, y=5+15f, z=-2+6t,…

A: Shortest distance between two skew lines