(c) Let F(x, y, z) = x³i+y³j + z³k. Compute the following:(i) V-F(ii) V x FXB)(d) Give one example to illustrate that vectors satisfy the triangle inequality Justifyyour answer.Question Two(a) Prove that the vector field F(x, y, z) — (x² + yz)i – 2y(x + 3)j + (ry + 2)k isincompressible, and find its vector potential function.

Since you have asked multiple question we will solve the first question for you. If you want any…

Answered: (c) Let F(x, y, z) = x³i+y³j + z³k.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q1. Consider the following vectors: ---C-(C)-C) 1 2 3 (a) Do the vectors u, v, w span R³7 (b) Is vector p in span{u, v, w}? If it is, find the coefficients #1, #2, #3 of a linear combination p= x₁ + x₂ + x3W
If you could show steps not just answers please
Q2/ A- If this vectors are perpendicular? Prove that. A= 3i +j- 4k B- 2i- 2j + k B- Solve that
[2₂] -2 two vectors in R². (a) U₁ = U1 V = - [2] and U₂ = 3 [2] be -2 Determine whether belongs to span {V₁, V₂} (b) {V₁, V₂} span R². Determine whether
(b) Check whether u = 6i – 2j+k and v =-4i –3j+9k are parallel or not. Then, find the area of triangle between both vectors.
What is î x (î × (î × (î + x)))? What is (x + ŷ) × ((& + ŷ) × )? Consider two vectors Ã and B. Write |Ã+ B| in terms of the length of Ā, the length of B, and the dot product of A and B.
-0---0 = 1. Which of these vectors is in the span of ₁, 2, 3? Justify your answers. For this entire problem set, consider the vectors #₁ = (a) -B (b) B -B (c) 2. (a) Describe the span of ₁, 2, 3 as a set of points in R³. (b) Is the span all of R³? 3. (a) Show that ws is in the span of ₁, ₂. and 3 = (b) Suppose 6 = 2w1 + ₂-33. Without calculating 6, show that b is in the span of w₁, 02. (c) Now calculate b using the given linear combination and using the linear combination you found. You should get the same vector.
Why is the cross product of two vectors axb always equal a vector ?
snip
-6 B-E- || List five vectors in Span {V1, V2}. Do not make a sketch. -4
I need you to answer the top question where it says: The vector u = (3180, 2450) gives the numbers of hamburgers and hot dogs, respectively, sold at a fast-food stand in one month. The vector v = (2.25, 1.75) gives the prices (in dollars) of the food items. Find the dot product u v. I have already answered the multiple choice questions, so please dont answer that. thank you

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(c) Let F(x, y, z) = x³i+y³j + z³k. Compute the following: (i) V-F (ii) VxF (d) Give one example to illustrate that vectors satisfy the triangle inequality Justify your answer.