Triangle ABC is bounded by x- axis, y-axis and line y = 12 – x Used Vector analysis to find the area and the coordinate of center of Triangle.

Q: represent the plane curve by a vector- valued function. (There are many correct answers.) y=(x-2)2

A: We have to represent the plane curve by a vector- valued function y = (x - 2)2

Q: Whereas a sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

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Q: What's the work, W, done by a force, F= -2i+10j lb in moving an object from a straight line from…

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Q: Find the area of the triangle determined by the points P, Q, and R. Find a unit vector perpendicular…

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Q: True or False Work is a physical example of a vector

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Q: How is vector calculated? What techniques/rules are used to find vector equation?

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Q: Dilate the vector (-2,6) by a factor of one half. K[ ? ],[ ]) Enter

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Q: O Represent the parabola 4=2文+1 by a vector valued funchion and sketch it (show everything !)

A: A parabola is a conic section. When a plane parallel to another plane and tangential to a right…

Q: Find the cross product of the unit vectors. Sketch your result.

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Q: Using vector methods, prove directly that if two sides of a quadrilateral are parallel and equal in…

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Q: Div curl A = 0 vector and curl grad q =0,where qis scalarfuction 0 صواب ihi O

A: True

Q: Fine the Vector function that represents the curve of intersection of the two surfaces. The cone z=…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: let angle thetha be measured from x1 axis counterclockwise to a line drawn normal to the boundary…

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Q: Magnitude of scalar multiple Prove that |cv| = |c| |v| , where c is a scalar and v is a vector.

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Q: cpmpute the volume of the parallelepiped defind by the vector v1(1,3,1)  v2(2,1,-1)  v3(1,0,1)

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Find divergence the vector A (div A) where (A=xz^2+ 3xyz) at a vector (1, * 2, -1)

A: Let's find.

Q: sketch the space curve represented by the intersection of the surfaces. Then represent the curve by…

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Q: Zero component of the curl For what vectors n is(curl F) ⋅ n = 0 when F = ⟨y, -2z, -x⟩?

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Q: Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v as…

A: Consider a parallelogram formed by the vectors u and v. Find the area of the parallelogram. Area of…

Q: ia vector-valued function whose graph The ellipsoid 9 = 1 49

A: r(u, v) = 3 sin(u) cos(v) i^ + 7 sin(u) sin(v) j^ + cos(u) k^

Q: Find a unit vector tangent to the curve of 25 intersection of – x? – 2y3 = z - 3 and 4y – 3z? =- x+…

A: This is a problem of vector calculus.

Q: Dot product from the definition Compute u ⋅ v if u and v are unit vectors and the angle between them…

A: We know that, dot product of two vectors u→ and v→ can be given as u→·v→=u→v→cosθ Where u→ and v→…

Q: Using

A: We use Vector Method.

Q: A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

A: Given :-  A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

Q: Column unit vector on the plane 2x + 2z - 4y = 3 is the vector

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Q: Three forces are applied to the triangular plate such that their lines of action are tangent to the…

A: Sum of moments about point O

Q: 11. It is the distance of the point A on the terminal side of angle in standard position from the…

A: Option C

Q: Vector v with initial point P = (x1, yı) and terminal point P, = (x2, y2) is equal to the vector v =…

A: Initial point is P1=x1, y1 and terminal point is P2=x2, y2.

Q: What are the vector and parametric equations for ideal projectile motion? How do you find a…

A: The vector equation and the Parametric Equation for ideal projectile motion :

Q: (a) Find the direction for which the directional derivative of the function f(x, y) = 9xy + 2y is a…

A: Formula for directional derivative Du→fP=∇f(P).u^=∇f(P)u^cosθ Du→fP to be maximum angle θmust be 0.…

Q: A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

A: Let us assume that : z=h1z=h2h1>h2 The surface area of the cylinder = 2πh1-h2 For sphere ,…

Q: The vector v and its initial point are given. Find the terminal po v= (2, -3, 6) Initial point: (0,…

A: Given vector is: v→=2, -3, 6 Initial point is: a0, b0, c0=0, 6, 1

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

Q: ta point a = (2, 4, 5). Find a non-zero vector (just

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Q: Dot Product of two-unit vectors is a unit vector. True False

A: Concept used: Consider two vectors as A→ and B→, then the dot product of these two vector is defined…

Q: LOCATE THtE NUMBERS 2 and z, vectorially (show your illustraton), APD uSE THっE vもCtDes TD 千ND A) 2,+…

A: Solution

Q: A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

A: Now we will place the sphere at the origin and the cylinder  with the z-axis as it's central axis.…

Q: Dot product from the definition Compute u ⋅ v if u is a unit vector, | v | = 2, and the angle…

A: To Determine:  Dot product from the definition Compute u ⋅ v  Given:  u is a unit vector, | v | = 2,…

Q: Evaluate the definite integral of the vector-valued function on the specified interval. (Your…

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Q: Compute the directional derivative in the direction of v at the given point. f(x, y) = exy=y, v =…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: To Determine: A net is dipped in a river .determine the flow rate of water across the net if the…

Q: Find the space curve represented by the intersection of the surfaces. Then represent the curve by a…

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Q: State the rules for di¡erentiating and integrating vector functions. Give examples.

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Q: Vector V has a horizontal vector component with magnitude 14 and a vertical vector component with…

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Q: Vector Calculus If r = xi + y) + zk, andr = ||r||, what is V In r?

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Q: Explain Properties of Vector Operations?

A: Query- Explain Properties of Vector Operations. Answer- There are two things required to defne a…