Reference no: EM132826506

Question 1 Given two vectors A = -a_x + a_y + 2a_z and B = a_x + Za_y + a_z, calculate A + B.
a) 3a_y + 3a_z;
b) -a_y + 3a_z;
c) -ax + 2ay + 2a_z;

d) 3.

Question 2: Given two vectors A = -a_x + a_y + 2a_z and B = a_x + 2a_y + a_z, calculate
A - B.
a) 3a_y + 3a_z;
b) -2a_x + 3a_y + a_z;
c) -2a_x - a_y + a_z;
d) -2.

Question 3 Given two vectors A = -a_x + a_y + 2a_z and B = a_x + 2a_y + a_z, find the vector component of A along B.
a) (-0.167, 0.333, -0.167);
b) (-0.167, -0.333, -0.167);

c) (0.5, 1, 0.5);
d) (.-33, -.667, -0.333).

Question 4 Given two vectors A = -a_x + a_y + 2a_z and B = a_x + 2a_y + a_z, calculate A x B.
a) -3a_x + 3a_y - 3a_z;
b) -3a_x - 3a_y + 3a_z;
c) -3a_x + 3a_y + a_z;
d) 5a_x, + 3a_y + a_z.

Question 5 Calculate a_z, x a_Ψ.
a) 0;
b) 1;
c) a_ρ;
d) -a_ρ.

Question 6

Calculate ax.ay.
a) 1;
b) 0;
c) -1;
d) a_z,

Question 7
Vector A is parallel to a line x = 2, y = 3. Determine the unit vector of A.
a) a_A = a_x;
b) a_A = ±a_x;
c) a_A = a_y;
d) a_A = ±a_z.

Question 8
Calculate a_x. a_x.
a) 1;
h) 0;
c) -1;
d) a,.

Question 9
Given two vectors A = -a_x + a_y + 2a_z and B = a_x + 2a_y + a_z, find the angle between A and B.
a) -60;
b) 60;
C) 90.6W;
d) -90.606

Question 10
Given two vectors A = -a_x + a_y + 2a_z and B = a_x + 2a_y + a_z, calculate A a B.
a) -a_x, + 2a_y + 2a_z;
b) -1;
c) -2;
d) 3.

Question 11
Given point P(0, I, I) and vector field G = xa_x, + za_y, + 2ya_z. Evaluate G in the cylindrical coordinate system at point P.
a) G = a_p + 2a_z;
b) G = 3a_p + 2a_z;
c) G = 2a_z;
d) G = -a_p + a_φ + 2a_z.

Question 12

Given point P(0 1, 1) and vector field G = xa_x + za_y + 2ya_z. If we wish to evaluate G in the cylindrical coordinate system at point P, determine the corresponding angle q).
a) φ = 0;

b) φ = Π/4

c) φ = ∞

d) φ = Π/2

Question 13

Given a scaler field V= ρz² + ρ² sinΦ + 2cosΦ we wish to determine E = - ∇V. Find E_z.
a) E_z = 2pz;
b) E_z = -2pz;
c) E_z = z² + sin φ;
d) E_z = cos φ - 2/ρ sin φ

Question 14

Given a vector field F = xya_x, - 3xza_y + yza_z, calculate ∇.F.
a) ∇.F = 2y + 1;
b) ∇.F = 2y - 3xy;
c) ∇.F = 2y;
d) ∇.F y + z.

Question 15

Given a scaler field V = ρz² + ρ²sinΦ + 2cosΦ, we wish to determine E = -∇V. Find E_p.
a) E_p = 2ρz;
b) E_p = cos φ -2/ρ sin φ;
c) E_P = z² + 2psin φ;
d) E_p = -z² - 2psin φ

Question 16

As shown in FIG. 1.3, the surface CDE belongs to an infinite plane. Describe this infinite plane.

a) z = 3;

b) z =5;

c) z = 0;
d) z = 0°.

Question 17

Given a vector field F = z²ap + ρ² sinφ a_z, we want to evaluate the surface integral of F through area AO& Define the differential area of this integral.
a) dS = -ρdρdφa_z;
b) dS = ρdρdφa_z;
c) dS = -dxdya_z;
d) dS = dxdya_z

Question 18

Given a vector field F = z²a_ρ + ρ² sin φa_z, evaluate the surface integral of F through area AOB.
a) Ψ_AOB = 2025;
b) Ψ_AOB = -20.25;
c) Ψ_AOB = 9;
d) Ψ_AOB = -9

Question 19

Given a vector field F = z²a_ρ + ρ² sinΨa_z, we want to evaluate the line integral of F along line DE. Define the differential length of this integral,

a) dl = pdφa_φ;
b) dl = dza_z;
c) dl = d_ρa_ρ;
d) dl = -d_ρa_ρ.

Question 20

Given a vector field F = z²a_ρ + ρ² sin φ a_z, calculate the line integral of F along line DE.
a) ∫F.dl = 112.5;

b) ∫F.dl = 75;
c) ∫F.dl = -75;
d) ∫F.dl = -112.5.

Attachment:- coordinate system.rar