Write a DAG model for computing the dot product between twon-dimensional vectors r and y.

Q: What is the relationship between vector subtraction and the basic vector operations of addition and…

A: What is the relationship between vector subtraction and the basic vector operations of addition and…

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. 1= (-…

A: We have to solve given problem:

Q: Find the angle between two vectors: A=31+4j-5k, (1) Scalar product. (2) vector product. B = 3i+4j+5k…

A: To find the angle between two vectors: A→=3i^+4j^-5k^, B→=3i^+4j^+5k^ by using: 1 Scalar product2…

Q: 23. Are the vectors u = and v = orthogonal? Explain.

A: Two vectors are orthogonal, if their dot product is equal to zero.  The formula to calculate dot…

Q: Explain why u + v • w _is not defined, where u, v, and w are nonzero vectors.

A: Given 3 non zero vectors : u , v and w. We need to explain why  u + v . w is not defined.

Q: 11) Use properties of vector to determine the value of the dot product å. b for the vectors ở = 21…

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Q: A three-dimensional unit vector parallel to the y-axis is

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

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

Q: Define the dot product (scalar product) of two vectors. Which al-gebraic laws are satisfied by dot…

A: Let (a1,a2,a3,....) and (b1,b2,b3,...) are two vectors. Then the dot product is defined by:

Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

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

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Q: Define the term Orthogonal vectors.

A: Given, Define the term Orthogonal vectors.

Q: Compute the distance between the vectors u = and v = 315

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Q: Write the Equation of a Plane in Vector form and Scalar form.

A: The equation of a plane in Vector form is given by n→·r→-r→0=0, where n→=a,b,c is a normal 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: Is the dot product of two vectors a scalar or a vector?

A: We know, Dot product of two vectors gives the product of the length of one vector by the length of…

Q: The two basic vector operations are scalar ________ and vector ________.

A: Our Aim is to tell the two basic vector operations.

Q: Write the vector as a linear combination of the unit vectors i and j.

A: Given two unit vectors i and j.  To write the linear combination of i and j.

Q: Explain why u + v ∙ w is not defined, where u, v, and w are nonzero vectors.

A: Let us assume that u,v, and w are nonzero vectors.  The dot product of the vector of the scalar…

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: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: Find the orthogonal projection of the vector onto the vector .

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Q: Describe all vectors v that are orthogonal to u

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Q: Find a unit vector parallel to the vector a´. a'= (-2,3,–1)

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Q: Find the projection of vector ū %3D

A: Given: a) u→=-i+5j+3kv→=-i+j-3k To find the projection of u→ on v→ b) To find the area of triangle…

Q: V. 3. V3

A: We have to solve given problem;

Q: The ________ ________ of two vectors yields a scalar, rather than a vector.

A: Given as  The ________ ________ of two vectors yields a scalar, rather than a vector.

Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: C a

A:

Q: Define the term column vector.

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

Q: Define the vector?

A: we have to define the vector.

Q: vector

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Q: Find the scalar and vector projections of b onto a, u

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Q: Write four forms of dot product for two vectors A and B by defining their metric tensor?

A: The dot product of two vectors, A and B in metric tensor form can be written as A→·B→=gμν aνbμ ,…

Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b= (3, 2, 1) compab projb=

A: Given a→=−3,−6,2 and b→=3,2,1 We have to find the scalar and vector projection of b→ onto a→. The…

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: 1. What is the appropriate dot product technique for both Cartesian and Geometric vectors?

A: Given

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u= (-11,0,5)…

A: To find the dot product and angle between the two vectors u and v.

Q: Explain why the vector 2u × 3v points in the same direction as the vector u × v.

A: Consider the vectors: u=x1i^+x2j^+x3k^v=y1i^+y2j^+y3k^

Q: Determine if the vectors u=, *v= and w= lie in the same plane or not

A:

Q: Determine whether the vector v = 8 is spanned by the vectors and 3 or not.

A: Given three vectors and we have to find if  v=789 is spanned by111 and 123

Q: Express the dot product of u and v in terms of the components of the vectors.

A: Express the dot product of u and v in terms of the components of the vectors.

Q: Illustrate and explain how to compute the vector product of two vectors.

A: Given query is to find explain vector product.

Q: Use a dot product to determine whether the vectors u = ⟨1, 2, 3⟩ and v = ⟨4, 1, -2⟩ are orthogonal.

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Q: Use the vectors u= (3, 6), v=(-6,5) to find the indicated quantity. State whether the result is a…

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Q: Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i-…

A: We have to find whether the given vectors are parallel, orthogonal, or neither by using the dot…

Q: Determine the dot product of the vectors а 3 (-3,—2, 3), b %3D (2,1,-2). b = (2,1,–2). a = 1. а:b —…

A: Solve for dot product

Q: a b

A:

Q: Find the scalar and vector projections of b onto a. (4, 7, -4) ь 3 (3, -1, 1) a

A: a=4, 7, -4, b=3, -1, 1 1. Scalar projection of b onto a is Proj ba. Proj ba=b·aa          =3, -1,…