Consider a vector given by E = (4xy + z)a, + 2x²a, + xa. Find the line integral B from A(3, 7, 1) to B(8, 9, 2) by (i) evaluating the line integral VAB E dl along A -B the line joining A to B and (i) evaluating {- E · dl E · dl E dl C D where the stopovers C and D are C(8, 7, 1) and D(8, 9, 1).

Q: Quèstion 30 The vector fields are defined as A= ap +2ag +3az, B В - 0 4aap +0.4Bao 6az, both vectors…

A:

Q: Given E = 5ax + ay - 3a, and F = -ax - 7ay - 2az. Use the vector algebra to find: (i) a unit vector…

A:

Q: A vector field is given by A = 3xyî - y ĵ. Find J. A .dl. where 'c' is the curve y = the x-y plane…

A: Given values are - A→=3xyi^-y2j^Curvey=2x2Pointx,y from 0,0 to 1,2

Q: e 5. Find the resultV • divergence of the vector D when D = e-* sin y î+ e¯* sin y ĵ fqa (1,“, 11)…

A:

Q: Prove that

A: If magnitude of F is 1 then unit vector. and if A.B=0 then perpendicular.

Q: The following vectors are given: M=-10ax+4ay-8az and N=8ax+7ay-2az. Find the unit vector in the…

A:

Q: Given two vectors A = 4ax + 2.5ay – 2az and B = 5ax + 2ay + 4 az . find (a) the angle between vector…

A: It is given that: A=4ax+2.5ay-2azB=5ax+2ay+4az

Q: Problem [2] In the figure below, write F= 1000 lb in the Cartesian vector form. 6 ft 4 ft A F-1000…

A:

Q: Question 7 Integral of Vector A= 2p sin(@)ap +0.5z?cos(9)az along L1 L2 L1 180° L3 30° -5 12.5 20…

A:

Q: Find whether the vectors are parallel, (-2,1,-1) and (0,3,1)

A:

Q: Need urgently

A: According to question:

Q: A vector field representing wind speeds is given by v = 3z®y? î + 4z*j. A walker can take one of two…

A:

Q: A = y²ââ + (2xy + 2²)ŷ + 2yzê¯

A: So we have to find the divergence.

Q: The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In…

A: According to the question, the vector field F is shown in the xy-plane and looks the same in all…

Q: If AB(1,2,-2) is not unit vector then the unit * vector is

A:

Q: 7. Determine the angle between the two vectors. a) A = and B = b) A = -2î+3j + 5k and B = i + 2j -…

A: As per the guidelines of Bartleby we suppose to answer first question only since you uploaded a…

Q: Question 9 Consider the vectors A =4ag+2ka, ta, and B = ag+4ay-16a, what value of k the two vectors…

A: Given  Find the value of k

Q: Given the vector filed A= a, + (2xy+ x2 +z9 ay +(4x+ 2yz) az. The divergence of the vector field is…

A: Divergence The scalar result of the administrator del and a given vector, which gives a proportion…

Q: Determine the divergence of a given vector field: D= (2xyz – y?)a + (x²z – 2xy)ay + x*yaz at PA(2,…

A:

Q: (1 Dz î V x B= db y + M.EDE VXB MEDE at colo = 10/0 ə az = (1 M.E. DE Ea at D B O 32B) -4 (0-0) +k…

A:

Q: Solve the given integral when c is a perfect circle to get a relation between H vector and I .

A:

Q: Given A = 4a + a_and vectors B = 2a_ + 3a , find the scalar projection of A on B.

A: The detailed solution is provided below.

Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, – 7.5az, Show that A and B are dependent vectors.

A:

Q: By applying the knowledge illustrate with help of a vector diagram equation Vs=Vreq+jVxeq for…

A:

Q: Q1) Find two unit vectors that are parallel to the xy- plane and are orthogonal to the vector w=āx -…

A:

Q: If A=2xz², what is the curl of this vector, V XA, in Cartesian coordinates? B 222 xz² -îz² -ŷz²

A:

Q: Q4. Find the angle that the vector A = 3î – 4ĵ makes with the positive x-axis Q5. Show that the…

A: The solution following questions are

Q: ). The divergence of a vector is vector AND (1). The curl of a vector is a scalar. a.Statemet () is…

A: Divergence of a vector results into scalar. As divergence is dot product. Dot product results into a…

Q: Which is the equivalent vector cylindrical components for cartesian vector G = [30, -40, 50]

A:

Q: The vector fields are defined as A= ap +2ao +3az, B= 0.25aap +0.25ßam -6az , both vectors are…

A:

Q: Q5. Integral of Vector A= p sin(@)a +z?cos( q)az along L1 L2 L1 180° L3 30° -5 10 -6.25 6.25

A: For the diagram shown below, the radius of the curvature is ρ=5 and the curve is lying on the x-y…

Q: If position of vectors of the points 2i+j-k and B = 5i + 4j + 3k, find |AB|.

A: Step 1: Step 2: Step 3: Step 4:

Q: Given the vector field H = xy²zax + x²yzay + xyz²ą, express it in cylindrical system at point (3,…

A: It is given that: H=xy2zax+x2yzay+xyz2az Points(3,-4,5)

Q: The dot product of two vectors

A: Dot Product  Let vector a¯=a1,a2,a3b¯=b1,b2,b3 The DOT product of vector a and b is given as…

Q: find tho Cur of he Vector function Sin a.

A: In this question we need to find a curl of the given vector.

Q: The sum of 2D RCS vectors (A + B) is equal to 7a, + 13a, while their difference (A - B) is equal to…

A:

Q: +3az , 0.5dap +0.5ßað -baz , both vectors are parallel then a and B are respectively (-4,-8)…

A:

Q: A Vector Field B = î cos (4) + forsin (6) exists in the closed Contour region show in the tragram…

A: According to the question, a vector field  exists in the closed contour region as shown belowWe need…

Q: Q4. Which one of the following vector function has divergence and curl both zero A 2xza, – yzay 2 az…

A: vector field F=⟨f,g,h⟩ Divergence of a vector function F is: The Curl of a vector function F is:…

Rectangular Coordinate System

In a rectangular coordinate system, each point based on the pair of coordinates is specified uniquely in the plane. From two fixed perpendicular lines, these coordinates are at a distance in the rectangular coordinate system. Each line is known as the reference axis and axes as plural. The point where they meet is called the origin (0,0).