4. This question is about dot products and normal forms. (a) Give an interesting example of a hyperplane H≤Rª in normal form. Interesting in this context means that the normal vector should have all entries different from zero. (b) Explain how to write the hyperplane in (a) in Cartesian form and vector form step by step.

Q: What is a vector?

A: A quantity that has magnitude as well as direction is called a vector.

Q: Find the unit vector in the direction of <4,2>

A:

Q: Explain how vectors written in component form are added or subtracted.

A: Vectors written in component form can be added by adding the corresponding components of both the…

Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: What is the zero vector?

A: We have to define

Q: How are a vector and a scalar different?

A:

Q: what is the graph of vector B = C - A??

A: First we mark A and C vectors then we find -C vector  The resultant of A and -C will be B as B = A -…

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

A:

Q: Why is HE vector twice of vector V?

A:

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: Explain an example of vector space.

A: In this question, we have to explain an example of vector space. Vector space :  An Abelian group…

Q: Find a vector orthogonal to both and . Please provide a detailed explanation of the process to get…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are write both vectors in…

Q: Express the following vector as the product of its magnitude and a unit vector: v=(3/5)i^ + (4/5)k^

A:

Q: what if it was the same vector, but 5y^2j?

A:

Q: Which vector in two-dimensional space has no corresponding unit vector?

A:

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: Describe the result when a point or line is changed by a vector

A: We will describe this.

Q: Write out the expressions a- Va in index notation for vector a

A: Let us consider a vectora→ = a1i^ +a2j^ +a3k^where a1 , a2, a3 are functions of (x1, x2 & x3)and…

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

A:

Q: A vector with magnitude 7 points in a direction 295 degrees counterclockwise from the positive x…

A:

Q: Given u = and V = , find 2u + 3v. O a) Ob) Oc) Od)

A: Given,  u=4,-3v=-1,2 Let's compute  2u=24,-32u=<8,-6> and  3v=3-1,23v=<-3,6>