27. Let u (10, 4) and v = (2, -5) Calculate the dot product u v. Show work. (b) Determine the angle between u and v. Round the result to the nearest degree (c)

Q: The angle between two planes is the smallest angle 0 between the planes 6x + 2y – 4z = 0 and - 7x +…

A: We will solve the problem

Q: The distance from (6,-5, 1) to yZ-plane is OA 6 /26 OC 1 O D. 62 OE 5 В.

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Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

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Q: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: 2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi-…

A: We have to the value of integral.

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: Calculate the distance between the points L= (8, 0) and K= (1, –4) in the coordinate plane. Give an…

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Q: 5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b.…

A: Given: (a). two lines l1 and l2 (b). Two Planes (c). A point (1,2,3) and a line  To Find: (a).…

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

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Q: When is An angle in the xy-plane is said to be in standard position?

A: An angle is in standard position if its vertex is located at the origin and one ray is on the…

Q: The distance from (4,-5, 10) to yZ-plane is O A.4 O B. 5 C. /141 OD.10 OE. 125

A: Solution is given below:

Q: Q: To find an angle between planes 2x + 4y - 4z- 6 = 0 and 4x + 3 y+9=0.

A: We have to find the angle between the given two planes.

Q: Use Eq. (8) to find the distance from Q = (1, 1, 1) to the plane2x + y + 5z = 2.

A: Find the distance from Q=(1, 1, 1) to the plane 2x+y+5z=2 or 2x+y+5z-2=0.…

Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

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Q: What is the sketch the phrase "three collinear points and a fourth point not on the line of the…

A: Introduction: Dual of any phrase can be find by replacing the conjunction connective with…

Q: Find the angle between the planes 3x-6y – 2z = 15 and 2x +y – 2z = 5

A: Recall: Vector method, cos θ=n1·n2n1n2 We have, n1=3i-6j-2k, n2=2i+j-2k

Q: Find the equation of the plane which passes through O and is parallel (5а + бу) — 3 to z – %3D

A: The equation of given plane is,      z - (5x + 6y) = 3⇒ z - 5x - 6y = d   for a plane of the form ax…

Q: ARST is reflected across a line so that T'has coordinates (1, 3). What are the Coordinates of S'? R…

A: Given: R=-4,4S=0,-2T=-3,-1

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

A:

Q: Find a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

Q: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

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Q: Find the condition for the points (a, 0), (h, k), (0, b)when ais not equals to U to be collinear

A: We have to find the condition

Q: Region A is formed by bounding the lines y= T, y = 6, and the y-axis. Determine which pair %3D of…

A: Region A is formed by bounding the lines y=x, y=6 and y-axis. We have to determine which pair of…

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: 3. Determine the angle between the planes: x - z+7=0 2x +y-z+8 = 0

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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: 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: 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: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

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Q: +4z=8 and

A: The equation of the plane as, x+z=1orx+0y+z=1 Here, a1 =1,b1 =0,c1 =1. and x+2y+4z=8 Here, a2 =1,b2…

Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

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Q: B. Show that line -- is parallel to plane x-2y+z = 6

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Q: to evaluate the line 12) Use Gren's Theorem integead along the posticy orientrch curre Jxy²dx…

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

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Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

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Q: Find angle between two planes given by 2x + y – z = 29 and 3x + y + 2z = 6. %3|

A: we have to find the angle between the two planes given by 2x+y-z=29 and 3x+y+2z=6. the equations of…

Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

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Q: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

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Q: Find the angle between the line 2 x+v3 : = z + 1 and the plane vZx + y + z – 2 = 0.

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Q: 17. Find the angle between two planes below. a. 2x- y+= =5 and 3x + y-z =1 b. 2x - 4y + 6z = 1 and…

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Q: 2 Let w = z². Find the image of the first quadrant in z-plane

A: