The value of the chiral vector of SWNTs if the n=8 , m=6 and the first vector length equal n/2+1 and the second vector length equal m/3+n/2

Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: What are the components of vector p which has three times the magnitude of the normal vector of the…

A: Given plane: Let the normal vector be n. So,

Q: find a vector parametrization for the line with thegiven description.Passes through P = (1, 2, −8),…

A: Find a vector parametrization for the line with the given description. Passes through P = (1, 2,…

Q: A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

A:

Q: Find Pakametriceq4atiobs for the lihes e1- The lihe through the origih Parallel to the Vector 2j+K…

A: h

Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

A: The vector parametrization is:                                       r(t) = r0 + tv = x0,y0,z0 +…

Q: Two Electric field vectors E1 and E2 are perpendicular to each other; obtain its base  vectors.

A:

Q: 4.) Correct of K vector representation for of terms B the velatie. positive normal and tangential…

A:

Q: 4. If p, 0, z are cylindrical coordinates, show that grad (log p) and grad o are solenoidal vectors.

A: In cyclindrical coordinate systemx=p Cosϕ , y=p Sinϕ , z=zP≥0 , 0≤ϕ<2π , -∞<z<∞dx=dp Cosϕ -…

Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: 5- The value of the chiral vector of SWNTS if the n=8, m=6 and the first vector length equal to +1…

A: n=8 m=6

Q: 3. fimdia a.A. vector.artheogenal.te. xv.and. Txw. b. A vectore.or.thogenal.b. und. SA…

A:

Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

A:

Q: Obtain a vector orthonormal to the vectors i−j  and (1, 0, 1)

A:

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

A:

Q: find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: A. If x and y are orthonormal vectors, then find the value of x+ yll- x-yll

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: Find the Values of h for which The vectors are Gnear dependent and Independint. -3 8.

A:

Q: If the vector K az+Lay+ Ma, shows the maximum increase rate and direction of the scalar V at point…

A:

Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=<0,-2,1>Hence, Vector…

Q: What is the magnitude of the vector v with initial point P = (-4, 3) and terminat piont Q = (2, -5)…

A: A detailed solution is given below

Q: ransform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates

A: For the vector given by xi+yj+zk. For the cartesian coordinates P(x,y,z),the corresponding…

Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

A:

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

A:

Q: Show that the vectors a = 3i+ 4j and b = 4i - 3j are perpendicular. A smooth sphere A of mass 2m…

A: Consider the given: a→=3i^+4j^b→=4i^-3j^ mass M of sphere A=2m velocity of sphere A of mass…

Q: 2. If A is the position vector of the point p-(x,y,z) and A=A. And ifr is the radius of the point in…

A: We apply the cross product to find the given function and simplification needed.

Q: Find the work done in moving a particle from point P(- 5, 0, 2) to Q(3, - 1, 4) if the magnitude and…

A: To find the work done in moving a particle from point P-5,0,2 to Q3,-1,4 Also the magnitude and…

Q: ir kümelerinden kaç tanesi R' için bir tabandır? how many of the given vector

A: A subest S of R2 is a subspace if and only if it contains the null vector whenever it contains two…

Q: In what direction should one move from the point (2, 3) to increase 4x?y most rapidly? Present your…

A: The solution is given below

Q: The relations between the unit vectors are ô, = ( sin 0 cos 4)ô, + ( sin 0 sin ø)ô, + ( cos 0)8, do…

A: We need to derive expressions A. 6-31, A.6-32, and A.6-33 by considering that A. 6-28, A.6-29, and…

Q: Compute the cosine of the angle between the plane through P – (6,0,0). Q = (0, 5,0), and R = (0,0,9)…

A: (a). Given points are P6,0,0, Q0,5,0 and R0,0,9. We know that equation of plane through a,0,0, 0,b,0…

Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

A:

Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A:

Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

A:

Q: 9. Find the normal unit vector n to the surface 62 + 2y²+ 2² = 225 at the point P: (5,5, 5).

A:

Q: 1. The path of a partide i3 qiven by Sut) =<3 lose, a thint 7 find a) Velouity vector and…

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find the magnitude of the projection of (7, 7) onto the vector (0, 9) Round your answer to at least…

A: Given 7,7 onto 0,9

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: Find an expression for a unit vector normal to the surface x = 10 cos (0) sin ($), y = 5 sin (0) sin…

A: Given that x=10cosθsinϕ, y=5sinθsinϕ and z=cosϕ. We have to find a unit vector normal to the…

Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: The surface of a hill can be given as h(x, y) = e-(z²+y²), If a ball is placed at the (2, y)…

A:

Q: Two out-of-phase alternating voltages are represented by: = 3.4sin (wt +) and V, = 1.3cos (wt +).…

A: we will find horizontal and vertical component of each voltage and then represent them in vector…

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: