Find a unit vector (i.) parallel to the graph of f at the given point f(x)=x^2+2x-4, (2,4) (ii.) perpendicular to the graph of f at the given point. f(x)=x^2+2x-4, (2,4)

Q: The directional derivative of the functionf (x, y) = -y at the point (–3, –2) in the direction of…

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Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: Definition used -                       If we have to write a vector as a linear combination of…

Q: The natural domain of a vector-valued function is the intersection of the domains of its component…

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Q: State two important features for a set of orthonormal vectors

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Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: what are the examples of contravarient and covariant tensors?

A: Example of Covariant tensor: A'i=aijAj

Q: (6) calculate the inrtantanco us rate of at point (4,1,2) in the change of 9 direction of the vector…

A: This is a question of multivariable calculus, the calculus of several variables.

Q: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

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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: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

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Q: 3. Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

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Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction…

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: Starting from the point (1, 2), at which direction does the above function f increase fastest? In…

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Q: Find the maximum rate of change of f(x, y, z) = x+ y/z at the point (-3, -3, -1) and the direction…

A: We have to find the maximum rate of change of fx,y,z=x+yz at -3,-3,-1 and the direction in which it…

Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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Q: How do I take the derivative of vectors and matrices?

A: To explain how to take the derivative of vectors and matrices.

Q: What is vector-valued function?

A: What is vector-valued function?

Q: What is the component form of the vector with an initial point of (-2,5) and a terminal point of…

A: Given that ,  The vector with  Initial Point = (-2 , 5) Terminal Point = (7 , -3).

Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal…

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Q: Find the directional derivative of in the direction of the vector (1,3) at the point (-1,2)

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Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: Sketch the gradient vector ∇f (4, 6) for the function f whose level curves are shown. Explain how…

A: To draw the gradient vector at a point, determine the direction and the length of the vector. The…

Q: A vector whose initial point is at the origin is called ---------------------------- a/an vector.

A: The given statement is " A vector whose initial point is at the origin".

Q: If a vector gets multiplied by a positive number, its direction will be .reversed F TO

A: To check: Whether the statement “if a vector gets multiplied a positive number its direction will be…

Q: The natural domain of the vector-valued function  is

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Q: 3. find the length of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2)

A: Solution :

Q: Create a vector-valued function whose graph is an ellipse, centered at (1, 2) with horizontal major…

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Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A: It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vector…

Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: Find the directional derivative of F(x,y,z)=x3y+4y2z+3xz3 at the point (3,-1,2)   in the direction…

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Q: Prove the two Scalar Multiple Rules for vector functions.

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Q: Express vector v with initial point P and terminal point Q in component form

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Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

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Q: What is the component form of the vector whose tail is the point (-3, 2) and whose head is the point…

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Q: How can one use a vector-valued function to represent a curve in two dimensions?

A: a plane vector consists of two quantities: direction and magnitude. Given any point in the plane…

Q: Dilate the vector (-3,5) by a factor of 3.

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Q: Evaluate the directional derivative Duf (2, 3) if ƒ (x, y) = and u is the unit vector in the same…

A: Given problem:- Evaluate the directional derivative Duf(2, 3) if f(x, y) = x/(x2 - y) and u is the…

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Prove the Sum and Difference Rules for vector functions.

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Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

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Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…

Q: What does the gradient vector of a function represent? Create your own real-life example that…

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