7. Find divF and curlF if (₁. (b) F = · (x² + y²)i + (y² + z²)j + (x² + z²)k. 8. Find the gradient of a function F = xy² + z³y at point (1,2,3). 9. Find the dirvegence and curl of a function F = x²yî + y) +xzk at the poin (1,2,1).

Q: Define the term binormal vector?

A: Question:- Define the term binormal vector?

Q: 'S' is a collection of vectors. Show that the rank of S is equal to the dimension of Span(S). Please…

A: Let  is a collection of vectors. Now, let the rank of is equal to  (say).It's row reduced eschelon…

Q: State the main idea for the Newton form of the basis?

A: Let there is a polynomial.  The polynomials of Newton’s basis are defined as:

Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

A:

Q: Explain why there is no vector v such that × v =.

A: We explain why there is no vector v such that  <1,2,1> × v =<3,1,5>

Q: How to solve this equation y'''+2y''+4y'+8y=5e^(3t)+1 using Method of Undetermined Coefficient

A:

Q: Describe 2-dimentional vector addition for any scenario? Put your best example over here.

A:

Q: What is the advantage and disadvantage of "scale diagram method" for vector?

A: Advantages and disadvantages of scale diagrams are listed below

Q: Explain the term scalar.

A: Explanation: Given that, term scalar.

Q: We know that there are two ways to multiply vectors: the vector and scalar product. How about vector…

A: Vector division is not possible .

Q: I have the following vectors, I have a problem with understanding why one becomes 'a+b' and the…

A: Vectors are geometric objects with both magnitude and direction. We will consider two vectors, a and…

Q: Solve the problem. Describe all solutions of Ax = b, where []· Describe the general solution in…

A:

Q: 3. Write ū as a sum of vectors, one in the direction of and another orthoganal to a. 18 [4] -5 [3³]

A: The given vector .The objective is to write the vector as a sum of vectors one in the direction of…

Q: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

Q: What role does the curl of a vector play in an application?

A: We have to write the curl of a vector play in an application.

Q: Provide one application of the study of vectors to aviation

A: A vector quantity has both magnitude and direction. It can be represented geometrically using a line…

Q: Sketch your process of determining the vector and find its component form if 7 makes the angle of…

A: Here we can use easy method like spherical coordinates to solve this question. Here magnitude and…

Q: i. BC if x = 2 and y =2

A: In right angle triangle BOC.

Q: what is Scalar variable ?

A: A scalar variable is used for storing a value that has no internal component. The value may change.…

Q: 5 Aaron and Maya want to write the vector u = -5 as a linear comb -19 -2 1 V1 -2 V2 = 1 and V3 = 2…

A: The { v1 ,v2 ,v3 } is not a set of orthogonal vectors.

Q: Give one example to illustrate that vectors satisfy the triangle inequality. Justify your answer

A: Vectors of Triangle Inequality : u+ v≤u + v

Q: Dot Product Find the dot product of the vectors a = (1, 3, −4) and b = (–2,3,1)

A:

Q: 4. Find two vectors and such that (i) both and are perpendicular to = (1,0,-1) and (ii) is…

A:

Q: Are the following vectors linearly independent? Do they span R³? Justify your answers. ECHE 3 2

A:

Q: If a = (4, 0, -1), find a vector b such that comp₂b = 3. b = X

A: a=<4,0,-1>ab=3ab=a→.b→a→let b=<b1,b2,b3>

Q: 1 If vector is a unit vector, what is the x?

A: We will find the value of x as following.

Q: 5. Drop a vector from the set A {sin'x,-1,1, sin 5x} to make it independent in F(-00, 00)

A: A set is linearly independent if no vector can be written as linear combination of others.