123. If F is a vector point function and a is a constant vector then show that i) V (a · F) = (a-V) F +a x (curlF). ii) ▼ · (a x F) a (divF) - (a · V) F. •curlF %3D iii) V x (a x F) =

Q: Suppose that f: R² R² is a function such that f (1,2)= the linear approximation. (Use syntax like…

A: We have to estimate f (1.1, 2.01) using the linear approximation.

Q: Let(vector u)=(-2,-3), (vector v=(-3,-5) and vector w=(-2,-3). Find the vector x that satisfies…

A: u=(-2,-3)v=(-3,-5)w=(-2,-3)Calculating x:

Q: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when

A:

Q: What is the graph of r(t)=2 costi + sintj?

A: Vector-valued function : It is a function of the form  r(t)=f(t)i⏜+g(t)j⏜ or…

Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

A:

Q: Which vector is collinear with [2, -3]? [2, -6] O [-4, 6] O(-2, -3] O [12, 18]

A: We have to find the vector

Q: (d) Find the value of that makes the following two vectors parallel to each other: a=-zi+3j 6=3i-j…

A:

Q: Determine where the vector function r(t) = i + (14t) j is continuous. Use symbolic notation and…

A: Please see the below picture for detailed solution.

Q: Consider the following function. T: R2 - R3, T(x, y) = (2x², 3xy, y²) Find the following images for…

A: Let us consider the given transformation T:V→W then the transformation is said to be linear…

Q: A certified public accountant (CPA) has found that seven out of ten company audits contain…

A:

Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

A:

Q: What is vector-valued function?

A: What is vector-valued function?

Q: Let h(x, y) = x² + 3xy - 6y. In what direction does h increase most rapidly at the point (3, 2)? (a)…

A:

Q: Given the vectors ü = -i - 2j + 3k and i = - 2i + 6j – 3k. _17. The unit vector in he direction of v…

A: A unit vector perpendicular to a vector a→ is represented as follows: a^=a→a→

Q: Consider the vector-valued function. (a) Show that is continuous at t = -1. (b) Evaluate (R. RY(2).…

A: Like a scalar function, features like continuity and differentiability are also demonstrated by…

Q: Given the vector function: r(t)=(√2t,e¹,e¹) find T(t), N(t), and B(t) and simplify your final…

A:

Q: H is the set of all vectors x = X2 in R³ with the property that X3 X1 + x2 = 0 and Xi – x2 + x3 = 0.…

A:

Q: - Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in…

A:

Q: The answer I provided for (x-5)^2 is said to be wrong. Please help me rectify the problem. Also…

A:

Q: \ Let v = (v, v2) be a direction vector on a line . The number 8 %3D defined to be the slope of the…

A: This is a problem of geometry and vector algebra.

Q: 2. [-/16.66 Points] DETAILS Find the directional derivative of the function at the given point in…

A:

Q: If you have vectors x-[1 5 9 5] and y-[4 8 3 6] find 1- Wex'+y 2- R-(y')* 3- X+y 4- X.*y

A: Given that we have two vectors with four components X= [ 1 5 9 5] Y= [ 4 8 3 6]

Q: EFGH is translated 6 units to the left and 3 units up. y -1 1 2 3 4 5 6 7 8 x E(4, -1) H(6, -2) -1…

A: Initially coordinates of F are (0,-3) After translating 6 units to the left, coordinates of F will…

Q: QI) (Vector Functions) It travels in a straight line to the point (4, 1, 4), has speed 2 at (1,2, 3)…

A: We will solve the following.