Whereas a sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes perpendicular to the axis of the cylinder. Using vector calculus concepts, show that the sphere part and the cylinder part between the two planes have the same area.

Q: What is a parallelepiped? What is meant by the parallelepiped determined by the vectors u, v, and w?…

A: A prism, made of parallelograms; a polyhedron with six faces, each of which is a parallelogram.  The…

Q: Find a non-zero vector a perpendicular to the vectors [3] and ū = 2 1

A: Given, v→ = 372  and  u→ = 121   We have to find the non zero x→ vector perpendicular to both the…

Q: Find eguation of a Plane that an contains the vector: and and Z=3E

A:

Q: True or False Work is a physical example of a vector

A:

Q: Find the length of the vector. v = (0, 2) ||v| = %3D

A:

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

A:

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

A:

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: ii) Find the dot product of the vector a in part (i) with the displacement vector AB such that…

A: Given that  Following vectors  To find the dot product

Q: Determine whether the statement, "Although I expected vector operations to produce another vector,…

A:

Q: Using vector methods, prove directly that if two sides of a quadrilateral are parallel and equal in…

A:

Q: As a result of losing a tug-of-war match, Mr. T is in the middle of a ditch. A group of people…

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

Q: A force F = 2i -j- 3k is applied to an airplane with displacement vector D = i+2j + 2k. Express F as…

A: Let the force vector be F→=2i-j-3k and the displacement vector D→=i+2j+2k    F→=β1+β2   Here, β1 is…

Q: Expreas the unit vector dirccted toward the point (0,0, A) from arbitrary point in the plane --2. an

A: In this question, we have to find the unit vector toward the given point from the given plane the…

Q: Determine whether the vectors a = (1,2,3),b = (1,3,1),c =(2,2,2) plane? coplanar, that is, they lie…

A: Answer and explanation is given below...

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

A:

Q: cpmpute the volume of the parallelepiped defind by the vector v1(1,3,1)  v2(2,1,-1)  v3(1,0,1)

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A:

Q: Howed Find efuation fer fendicular to the vector from origin to A. of the plane through…

A:

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: 3. The dot product of two orthogonal vectors is: A.undefined. B. Zero, C. Infinity.

A:

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A:

Q: 2 nogonal to the vector

A: The coordinates of point M is 1,1,0 . The orthogonal vector to M is 200. The equation of the plane…

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

A:

Q: Using

A: We use Vector Method.

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

A: Given :-  A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

Q: Find a non-zero vector i perpendicular to the vector i

A: See the attachment

Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

A:

Q: (a) Find the vector projection of a onto b , that is, find proj, a . (b) Find a vector in the…

A: We can solve the problem problem using concept of vector.

Q: True or False A vector in space may be described by specifying its magnitude and its direction…

A: Answer: True.

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

A: Some information in the question is missing.

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

A: Let us assume that : z=h1z=h2h1>h2 The surface area of the cylinder = 2πh1-h2 For sphere ,…

Q: show that outer product for two vectors not rotation and not commulative ? justify your answer

A: The outer product is defined as, Consider x=x1x2x3⋮xn and y=y1y2y3⋮yn are two vectors from ℝn. Then…

Q: Describe the span ot the two vectors (1,0,9) and co. 1,15 geometricellyy in

A:

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: Let p and q be two non-zero vectors. By using the definition of vector product show that pxq =…

A: In the given question, calculate the area of the parallelogram where two sides p and q are given.…

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

A: Now we will place the sphere at the origin and the cylinder  with the z-axis as it's central axis.…

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: Charge is not scalar ylan O İhi O

A: We have to find that charge is scalar or not

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?

A:

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

A:

Q: If vector a= and vector b= .. are vectors a and b orthogonal, parallel, or neither? Provide…

A: Topic = Vector   2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

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

A: Follow the steps.

Q: A force of 40lbs acts on a body at an angle of 30°. Express the force vector in component form and…

A: Vector

Q: Show that a unit vector in the plane can be expressed as u = (cos u)i + (sin u)j, obtained by…

A: To show that a unit vector can be expressed as u = (cos u) i + (sin u) j.

Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

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: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…