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

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: Find the point at which the line T(t) = (4, 1, 7) +t( – 5, – 7, – 4) intersects the yz plane.

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Q: Find the intersection of the plane: x - z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: Find the point closest to origin in R³ that is on both the planes 3x+y+z=5 and x+y+z=1.

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

Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

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: Let 1, y E R². Show that p:=y is the closest point on the line Span(y) to z.

A: Given, x,y ∈ R2 To show: p=x.yy.yy is the closest point on the line span y to x

Q: For planes 2x + y – z = 2 and 2x + 3y + 5z = 4,

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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: Match the surfaces (a)-(e) with the contour diagrams (1)-(V, (M)

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Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

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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: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

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Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 &amp; C2 then substitute the x,y,z values into the line…

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: Show that if y is the boundary

A: To prove that if γ is the boundary of the trianglee with vertices at z=0, z=3i,and z=-4 oriented in…

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 shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: 5. In the standard (x, y) coordinate plane, the midpoint of LM is at (4, –4) and L is at (1,3). What…

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Q: .2 y = x", y = 2x, about the line x = 0 using the method of disks or washers. 4 Volume…

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Q: 2. Approximate f,(3,5) using the contour diagram of S(x, y) in Figure 14.9.

A: Given query is to find the value of fx(3,5).

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Which of the following represents two lines that are coplanar and do not intersect?

A: We want to find the lines which are coplanar and don't intersect.

Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

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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: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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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: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

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Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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Q: Suppose we have: u = and v = . Based on their relative positions in the xy-plane, in which…

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Q: I need help with b and e

A: The solution are next step

Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

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Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

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

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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: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

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: Show that the plances x + y – z = 1 perpendicular. and 2x – 3y + 4z = 5 are neither parallel nor

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Q: Graph the image of rhombus TUVW after a translation 5 units right and 12 units down. W 10 V U 4- 2…

A: given,         A rhombus TUVW,             T= (-8,6)            V=(0,10)           W=(-5,10)…

Q: and V is the dosed by the Planes x=0, y=O, ニこ

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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: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: Find the point of intersection between the planes TT :x+y-z =1, n, : 2x – 3y -9z = 10 and n, : x +…

A: The three planes are, π1=x+y-z=1 π2=2x-3y-9z=10 π3=x+2y-3z=-4

Q: Find the point(s) of intersection of the line l : ¯r(t) = ⟨−4, 3, 4⟩+ t⟨−5, 3, 4⟩ and the unit…

A: Solved below