Example 1-6 Express each of the three forces acting on the column in Cartesian vector form and compute the magnitude of the resultant force.

Q: Determine whether the vectors (4, 2, 3)T , (2, 3, 1)T , and (2,−5, 3)T are linearly dependent.

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Q: 11) (Section 9.5,9.6) Find a unit vector that is orthongonal to both u and u = (2,–1,3) v= (1,0, –2)…

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Q: State the main idea for the Newton form of the basis?

A: Let there is a polynomial.  The polynomials of Newton’s basis are defined as:

Q: التاريخ 5.1 1 1 If the vector [42] An with the straight Piecel the end point?

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Q: Example.2 Find a vector that is perpendicular to both A =i+j+k and B = i+j

A: We have to find a vector which is perpendicular to both the vectors.

Q: Show that the vectors below are independent. 1 3 3 3 5 3

A: The given vectors are 123,  -1-15   and  333. Compute the determinant of matrix formed by these…

Q: Let a = (-1; 3; 2) and b = (4; -2; 1). Find two unit vectors orthogonal to both a and b. Are the…

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Q: Question 1) Resolve the vector into its x- and y-components. 940N < 326° x=  y=  Round to whole…

A: For every vector, the x component is the cosine of that vector and the y component is the sine of…

Q: The three forces and the force pairs in the figure are Reduce to a resultant force

A: Given that,

Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

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Q: 1) Find the MAGNITUDE and DIRECTION of the RESULTANT of ALL the forces at point A

A: To find the magnitude and direction of the resultant force.

Q: 1. Sketch the vector v = (-2, 4). %3D 10f 4 2 10-8-6-4 -2 -6 -8 10 2. Sketch the vector v = 4i – 6j.…

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Q: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: What is the resultant of vector A=2i +3j. and vector B=3i -2j Select one: a. 3.5 O b. 2 C. 5/2 Od.…

A: A vector is something that has both magnitude and direction. Like, if you are saying, someone is…

Q: to = [0 3 4 2]" v = [1 1 2 1]"

A: Handwriting solution.  { v0, v1, e1, e4} forms a basis for R4.

Q: 5. Express the vector having magnitude 7, and direction 13 degrees (when drawn in standard…

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Q: 2. Find two unit vectors orthogonal to both and .

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Q: Find the magnitude of the given vector. (-3, 6, 2)

A: Given,            The vector is &lt;-3,6,2&gt;.To find : The magnitude of the given vector.We know…

Q: snip

A: If v = &lt;a, b&gt; is an algebraic vector whose initial point is the origin, then v is called…

Q: In the given diagram, which is the equivalent of vector

A: sum of vectors of closed triangle is 0 if we choose one direction -- Here if choose anticlockwise…

Q: 9) (Section 9.4) Find the magnitude of vector u = -60i+11j

A: Given,   u = -60i+11jMagnitude of vector ; u=-602 + 112u = 3600+121  = 3721 =61

Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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Q: 17 (c) Find a unit vector which is orthogonal to the vectors -1 2 and 1 -3 5

A: First we will find a vector which is orthogonal to both given vectors and then we will find the unit…

Q: 6. A student claims to have found a vector A such that (2i - 3j + 4k) x A = (4i + 3j - k). Do you…

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Q: snip

A: If F1 and F2 are two forces simultaneously acting on an object, the vector sum F1+F2 is called the…

Q: 19. Find two unit vectors orthogonal to both (3, 2, 1) and (-1, 1, 0). Answer

A: Unit vector orthogonal to both a⇀, b⇀ is: ±a⇀×b⇀a⇀×b⇀

Q: 4. Determine the resultant of each combination of vectors. a. 25 km/h north and 81 km/h east

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Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: Determine whether each collection of vectors is linearly independent or linearly dependent. Justify…

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Q: determine the magnitude of the vector ∥⟨2,8⟩∥

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Q: 19) (Section 9.7) Find a unit vector orthogonal to both vectors u = 2i + 5 j –k v=i+3j-2k %3D…

A: We know that the cross product yields the vector orthogonal to both vectors .Here…

Q: what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a…

A: A scalar is a real number. A scaler is a single, independent number.  A vector is a ordered…

Q: If vector A is any non-zero vector, a unit vector in the same direction of A would be?

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Q: If an object is stationary (at rest), then the sum of the forces acting on the objectequal the _____…

A: An object is at rest only when sum of all the forces acting on the object is zero.

Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

Q: Question 4: Find basis for R*, that contains the vectors vị 2 and 1 v2 = -1]

A: A basis to an n-dimensional space is a set of n vectors which span the space and are linearly…

Q: QUESTION 2 a) Use the Wronskian to show that the set of vectors {-2x + 1, e*, cos x}

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Q: Question 6 Two vectors are orthogonal if their inner product is equal to 90. True False

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Q: 1. what is the basic concept of a vector?

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Q: 2 Find The vector novmal to The vector A=2i-3;

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Q: 1. Determine the single positive vector that is the resultant of: CD ED + AB - CB D

A: Vector AB = - Vector BA

Q: Find the magnitude of the following vector. (-1, 2)

A: Given&lt;-1 , 2&gt;

Q: The number of elements in a vector generated by [4:0.1:13] is

A: We have to find the number of elements in a vector generated by  [4 : 0.1 : 13].

Q: Example 2: Find the unit vector in the direction of v = (-1,3,4) and verify that this vector has…

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Q: Suppose the vector x characterizing the antigenic state of an influenza virus population changes…

A: The vector in the previous influenza season is 3/2, 1

Q: EXAMPLE 2 Find a vector perpendicular to the plane of P(1, –1, 0), Q(2, 1, –1), and R(-1, 1, 2)…

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Q: Question 4: Find basis for R*, that contains the vectors vį = and V2 = -1] 1234

A: In the given question we have to find the basis of which contain the vectors . Concept: here we…

Q: Draw the vector within the unit cell (1.-2.-1

A: Given vector is (1,-2,-1). It can be written as, u⇀=i-2j-k. To draw the vector in the unit cell, we…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: