Find a function r(t) that describes the line passing through P(9,9,9) and Q(8,4,5). r(t) = (-t+9, - 5t + 9, – 4t + 9) , for 0 s t s 1 %3D

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 3x + 6y at the point…

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Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

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Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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Q: Find the directional derivative of f at the point (, 1) in the (V3, –1). (Hints : (a) It is faster…

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Q: Two unit vectors that are parallel to the tangent line to the curve y= 2sinx at the point (t/6, 1)…

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A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: Which of the next statements is false? the dot product of two vectors is a vector and the cross…

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Q: Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 2. Suppose that f (1,2)= 3 and that the directional derivative of fat point (1,2) in the direction…

A: Given that f1,2=3 and the directional derivative of f at point (1,2) in the direction of the vector…

Q: 2. Suppose the elevation of a hilly contryside is given by the function E(z,y) = sin z + cos y. %3D…

A: The solution of given problem is followed by

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: 2y +4 /5 -Зх — 5 -11 5 2у + 4 12 Ex: 5 : Ex: 5

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Q: An object is moving in the xy-plane along a path whose curvature at time t is given by the function…

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Q: Suppose that a particle following the path c(t) = (t,t – 5t,0) flies off on a tangent at to = 3.…

A: Given:c(t) = (t2 , t3-5t , 0)

Q: A firefighter is standing on top of a building 19 m high, holding a firehose 1 m above the top of…

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Q: 2. Suppose that f (1,2) = 3 and that the directional derivative of ƒat point (1,2) in the direction…

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Q: Suppose that f (1,2) = 3 and that the directional derivative of f at point (1,2) in the direction of…

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

Q: An object moves with velocity vector (t,t?,-t) starting at (1,2,3) when t=0. Find the function r…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: 1. True or False: It's possible for the directional derivatives of a given function along two…

A: Solution-1)

Q: The plane with normal vector - 7) containing the point (4,-1,1) has equation Ar + By + Cz = D. If A…

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Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) : 5x sin(xy)…

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Q: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: Find a function r(t) that describes the line through P(3,4,5) that is orthogonal to the plane…

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Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

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Q: Find a vector orthogonal to the line x+y=1

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Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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Q: An object is moving in the xy-plane along a path whose curvature at time t is given by the function…

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Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: Suppose you have data on two economiC variables, X1 and X2. You are interested in learning whnether…

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Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: Write down the vector equations of the tangent lines to the traces for /(r, 3) = re-y² at (2,0) for…

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Q: If F(x,y) is a differentiable function and the equation F(x, y) = 0 defines (y) as a function of…

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Q: Choose the direction vector for which the function f defined by f(x, y)= sin(3x) cos(11y) has the…

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Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

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Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: Match the vector valued function with its graph where 0 <t < 2n. Not all equations will be used. Use…

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: When is a vector incomprehensible and when is a vector irrational?

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Q: Prove that the vector T'(t) = 0 for moving in a straight line

A: Note that, the object's path is rt=xti+ytj. yt=mxt+b, where m and b are constant. It is known that,…

Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

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Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

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Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.