Derive the relation between unit Vectors of Glindrical and Cartesian Coordinates?

Q: Define the term binormal vector?

A: Question:- Define the term binormal vector?

Q: Whereas a sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

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Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

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Q: What is a unit vector perpendicular to these two vectors, which are two vectors

A: We have to solve given problem:

Q: How is the angle between two vectors defined and how is it computed?

A: the angle between two vectors is computed using cosθ

Q: Find the projection of vector ū = -i+ 5j + 3k onto the vector i = -i +j- 3k? %3D

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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: Define Dot Product of vectors.

A: The dot product (scalar product) of two vectors is the magnitude of the vectors and the cosine of…

Q: What is the difference between a vector and a scalar?

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Q: What is the dot product of a vector with the cross product that this vector has with another vector?

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Q: snip1

A: orthogonal to u means the dot product of the vectors should be zeroso v.u=0xy.31=03x+y=0from here we…

Q: Express the vectors in Exercises 9–10 in terms of their lengths and directions. 9. Velocity vector v…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find a-Vectak S unit, tengte inthedirectionofthe Vector A-ixjtk-

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Q: A vector with magnitude 8 points in a direction 280 degrees counterclockwise from the positive x…

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Q: What are the unit vectors in their component form?

A: Write the definition of the unit vectors that help to find their component forms. A vector is said…

Q: Find a unit vector perpendicular to both u = (2,3, –4) and v = (-1,1,–4). %3D

A: The unit vector perpendicular to u and v is given by: w=±(u×v)|u×v|

Q: What is the i-component of unit vector of the vector u ? Give your answer correct to two decimal…

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Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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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: A forklift is used to offload freight from a delivery truck. Together, the forklift and its contents…

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Q: Define the term Orthogonal vectors.

A: Given, Define the term Orthogonal vectors.

Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: Evaluate F - dS, where F = and S is the helicoid with vector equation r(и, о) - = 0 < u < 2, 0 < v…

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Q: A vector with magnitude 8 points in a direction 340 degrees counterclockwise from the positive x…

A: Given vector with magnitude 8 points in a direction 340 degrees counterclockwise from the positive…

Q: 2. Convert the vector A=10ax in the Cartesian Coordinates into a vector expressed in the Cylindrical…

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Q: The vector having (magnitude) only is called unit vector FO

A: GivenStatement:The vector having only magnitude is called unit vectorTo determineGiven statement is…

Q: Explain how you can convert from a plane's scalar equation to a vector equation.

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Q: A vector with magnitude 10 points in a direction 295 degrees counterclockwise from the positive x…

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Q: Explain with the help of an example whether the angle between vectors is acute or obtuse.

A: As the Angle Increases, the Name Changes: Type of Angle Description Acute Angle is less than…

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

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Q: Specify the unit vector extending from origin toward the point G(2,-2,-1). Graph a vector V in the…

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

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Q: How does translation T along vector AB affect the points in the plane?

A: Some information in the question is missing.

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: tind a non-zero vector perpendıcular to the vectar u. Find the length of the vector R-

A: Consider two vector u→=ai→+bj→ and v→=ci→+dj→ if the two vector is perpendicular then the angle…

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: How do you find a vector perpendicular to a plane?

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(15,0)

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Q: what will be four forms of dot product for two vectors A and B by defining their metric tensors?

A: Dot product of two vectors is given by the product of the magnitudes an cosine of the angle between…

Q: Vector ä has a magnitude of zo and poin ts 60' Norte of East. Caleulate the * and comporents of À

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

A: Follow the steps.

Q: What is a unit vector in the direction of u

A: Given,u= 40-3-12First calculate magnitude of u;So,  u=42+02+-32+-122                 =16+9+144…

Q: A vector with magnitude 4 points in a direction 265 degrees counterclockwise from the positive x…

A: Given  Magnitude of 4 points at an angle of 265° In counter clockwise direction  from positive x-…

Q: What is Vectors and vector addition? What are the vector components?

A: Vectors: A vector is what represents both magnitude and direction. Vectors can be decomposed into…

Q: Let vector u = and vector v . Find the magnitude of 3u-4v. Round to one decimal place.

A: Let vector u= &lt;3, 4&gt; and vector v = &lt;6, 7&gt; then find the magnitude of vector 3u-4v.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.