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

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Q: Define left singular vectors.

A: To Define:Left singular vectors.

Q: Describe all solutions of Ax = b, where 2-5 3 A -2 6 -5 70] and b = Describe the general solution in…

A:

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: Hiwil show that_Viz 3i+6j_and_V=-i-zj have offosite direction.

A: We have to prove that vectors have opposite direction.

Q: Describe all solutions 2 -1 3 -4 2-6-2¹] of Ax = 0 in parametric vector form if 11

A:

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

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Q: Why is HE vector twice of vector V?

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Q: Fill in the blanks with numbers to show that the vector is a linear combination of the ---

A:

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?

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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

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Q: Define the term vector.

A:

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

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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>

Q: Define the vector?

A: we have to define the vector.