What is the effect of scaling a Vector? Give an example?

Q: Define the term binormal vector?

A: Question:- Define the term binormal vector?

Q: What is a position vector? How is a position vector represented using i and j?

A: The position vector is a vector whose initial point is origin and and the terminal point is any…

Q: How are a vector and a scalar different?

A:

Q: a) Give an example of unit vector in R3.

A: Since  you have asked multiple questions in a single request we would be answering only the first…

Q: (a) Using Gaussian elimination, find a vector v such that

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one.…

Q: How do you know if 3 vectors span R^3? Is there any example?

A:

Q: How do you find the vector from one point to another?

A: The vector from one point to other is the difference between similar coordinates of two points.

Q: Explain when a projection vector is negative, positive, or zero.

A: This question is based on dot product of two vector.

Q: Explain how to write a vector in terms of its magnitude and direction.

A: A vector is a geometric representation of magnitude and direction with respect to the set of…

Q: Find the magnitude of the vector. (-3, – 7)

A:

Q: A unit vector along a

A:

Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: b) Give an example of 5 linearly independent vectors in R*, or explain why it is impossible to do…

A:

Q: How do you add two vectors algebraically? Geometrically?

A: Solution: Consider the two vectors: u→ = u1, u2 and v→ = v1, v2 Then the sum of u→ and v→is called…

Q: Define the term Orthogonal vectors.

A: Given, Define the term Orthogonal vectors.

Q: Explain the difference between an algebraic vector and aposition vector.

A: We have to explain the difference between an algebraic vector and a position vector.

Q: How do you find out the projection of a vector u on a vector w

A: Projection of vector u on w is nothing but the dot product of u and w divided by magnitude of vector…

Q: Determine the tail of the vector whose head is(1, 2). Make a sketch.

A: Given the vector 26 and tail of the vector is (1,2). We need to find the head of the vector.

Q: What is the vector translating A to B? B to A? What is the effect of a translation?

A:

Q: Find the magnitude of the given vector. (-3, 6, 2)

A: Given,            The vector is <-3,6,2>.To find : The magnitude of the given vector.We know…

Q: Normalize the vector

A: Given vector is v=  2-1  3

Q: (b) Sketch enough vectors in the vector field to get a sense of its geometric structure. (You should…

A: Given first order system of equation: dudt=u-1dvdt=v-1 the objective is to sketch the enough vectors…

Q: Determine if the vectors are linearly independent or not

A: The vectors are linearly independent.

Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: What is the different between linear dependent and linear independent vectors? Given any three…

A:

Q: Give the  3 characteristics of a vector

A: Three Character of vectors are given:

Q: How are vectors added and subtracted geometrically? Algebraically?

A: Vector Addition Geometrically:

Q: Find the magnitude of this vector (-8,8)

A: Given vector is  The magnitude of this vector is

Q: The amount of money currently in your bank account is an example of a vector. O True False

A:

Q: Define the term vector.

A:

Q: Determine whether the statement, "I used a vector to represent the average yearly rate of change in…

A: the statement does not make any sense.

Q: Define the term column vector.

A: Column Vector is defined as a column matrix representing the elements of any vector written in…

Q: Is (1, 1) a unit vector? Explain.

A: We know that if any vector a→=a1i+a2j+a3k will be a unit vector then its magnitude a→=a12+a22+a32…

Q: Determine if the vector is a linear combination of the remaining vectors. Explain the steps.

A: We will check whether the vector v is linear combination of others or not.

Q: How can you tell when vectors span a certain R^? Please explain in the most simplistic detail>

A: Let S=v1,v2,v3 And v1=1-12;v2=213;v3=-102 Does SpanS=ℝ3? if any vector in ℝ3 can be expressed or…

Q: Determine the tail of the vector whose head is (1, 2). Make a sketch.

A: Consider the provided vector, 26 Whose head is 1,2. Determine the tail of the given vector.

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

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

Q: Use the figure to sketch a graph of the vector. u- V y

A:

Q: Is it possible to take a dot and cross product of a scalar with a vector? Explain with example.

A: It is not possible to take a dot and cross product of a scalar with a vector.

Q: What helps to set of vectors linearly independent?

A:

Q: Which vector is the result of a + b?

A:

Q: 3. Determine if the vectors linearly independent or linearly dependent Please explain your answer…

A:

Q: Please provide a well explained answer for the follwoing. And explain what are the main features of…

A:

Q: Dot Product of a vector with itself is equal to the square of its magnitude. True O False

A: Follow the steps.

Q: Discuss the concept of vectors in engineering mathematics

A: Vector is an object which has both direction and magnitude. Vectors are used to represent quantities…

Q: Explain Properties of Vector Operations?

A: Query- Explain Properties of Vector Operations. Answer- There are two things required to defne a…