Show that the directions of the isoline and the gradient line at any given points in a scalar field are orthogonal to each other.

Q: The unit vector from A(4, 2) to the point B(-2, 10) is:

A:

Q: On more than two vectors. The first has a standard of 11m/s, the other a standard of 3m/s. All…

A: Given, resultant of vector A(say) = 11m/s resultant of vector B(say) = 3m/s So, sum of these two…

Q: Determine the divergence and curl of the following vector fields. Also graphically show that your…

A: Determine, The divergence and curl of the vector fields

Q: Use qualitative arguments (i.e., draw surfaces and/or loops on the plots and ascribe mcaning to the…

A: Loop drawn in the diagram shows that vector field has non zero divergence since net arrows are…

Q: The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) =,…

A: We can write the electric field as given by-…

Q: Find a) the position vector rAB from point A to B and b) the position vector rBA from B to A.

A: Given data, Point A (3,4) Point B (11,10)

Q: Given a vector (77, 48, 22) and another vector (4, 49, 67) what is the z-component of their sum?

A: Given that Vector 1 (A)= (77, 48, 22)  And , vector 2 (B)= (4, 49, 67) Let i, j and k be the unit…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A:

Q: The 3X3 matrix which is being made is having axis coordinates, point coordinates and the force…

A: Axis coordinates, point coordinates, and the force coordinates

Q: Find the arc length of the space curve given by the vector function r (t) t3 i + t2 j + (2t + 1) k…

A:

Q: Find a unit vector normal to the surface xy? + xz = 1 at the point (–1, 1, 1).

A: Given surface-xy2+xz=1P=(-,1,1)

Q: Given the points A: (2,-1,1) and B (0,-1,-3), find the vector u = vector AB.

A: The objective of the question is to find the vector u = AB given the points A: (2,-1,1) and B:…

Q: Determine the scalar components R, and R₂ of the force R along the nonrectangular axes a and b. Also…

A: Given that,  R = 760 N Angle, θ = 110° and Φ = 27° Another angle, q = 180° - (110° + 27°) => q =…

Q: Let 2 vectors å anb b a 121=53161-5 in the plane of modules. How much is the magnitude of their e…

A:

Q: The vectors ā, b and čare not planar. The a', & and d are the associated reciprocal vectors given by…

A:

Q: at the origin.

A:

Q: What is the angle between the two vectors i + 2j - 3k and 3i + 2j + k? Round your answer to the…

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solution:-

Q: Check if the gradient theorem is fulfilled by integrating f = x2 + 4xy + 2yz3 between the points a =…

A:

Q: are orthogonal.

A: Given that, A=4-3-25 and B=150k The condition of the orthogonality of two vector is given as, A⨥B=0

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Let F1, F2, and F­3 denote the three forces, θ1, θ2, and θ3 denote the three angles of the forces…

Q: For any two nonparallel and non orthogonal vectors a and b with angle between them, it holds that…

A:

Q: A vector field is given in spherical coordinates as B=RR² cos(6/2) + Rsin(0) sin(0/2) . Evaluate (V…

A:

Q: K is a vector field and V is a scalar field. The divergence of K is equal V; that is V = V.K.…

A: This problem is from Electrodynamics. Let's solve it step by step. Please have a good look Given…

Q: Suppose that you have two vectors (1,0,0, 1) (2,0,0, 2) at What is a"b,?

A: Given that aμ=(1,0,0,1) and bμ=(2,0,0,2) we have to find the value of aμbμ

Q: Express the vector field D = (x² + y²)−¹(xɑx + yay) in cylindrical components and cylindrical…

A: The cylindrical coordinates (ρ, ϕ, z) of a vector are related to its cartesian components (x, y, z)…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Given: The resultant magnitude R and the angle θ between the x-axis and the line of action of the…

Q: Find the vector component of v=2i−j+3k along b=i+4j+8k and the vector component of v orthogonal to…

A: