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: What is a vector?

A: A quantity that has magnitude as well as direction is called a vector.

Q: Find the resultant force of two vectors F = 5î + 2j and F = -2î - 8j. Graph the two vectors as well…

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Q: C A

A: We use Triangle law

Q: A vector with magnitude 6 points in a direction 190 degrees counterclockwise from the positive x…

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Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: How are a vector and a scalar different?

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Q: A vector has components A₁, A₂ and 43 in a right-handed rectangu The coordinate system is rotated…

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Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: A boat is motoring directly north at 5 miles per hour. At the same time, an 8 m.p.h. wind is blowing…

A: Since you have asked multiple questions,we will solve the first question for you. If you want any…

Q: A motorboat sets out at 10 am from a position (-6i – 2j) km relative to a marker buoy, and travels…

A: please see the next step for solution

Q: Find the unit vector in the direction of

A: Unit vector in the direction <-2, -5> Unit vector have magnitude 1

Q: The scalar multiplication of a vector by a positive value results in another vector having the same…

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Q: Find the unit vector with the opposite direction of a⃗=(8,−10,3,−1,9,3)

A: We have to find the unit vector with the opposite direction of a→=8,-10,3,-1,9,3.

Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

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: What is the vector j?

A: We have to tell what is vector j   it is also written as j→

Q: Find the scalar component of 6 a, +2 a,-3 a, along 3 a,- 4 a,

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Q: Resolve the vector a = -i+ 4j+9k into orthogonal vectors, one of which is parallel to b =i- 3j – k.

A: Given vectors are a→=−i^+4j^+9k^ and b→=i^−3j^−k^. Here, we using the concept of projection . We can…

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: