Assume the following position vectors. r A B = 0 i + 0 j + 8 k r A C = − 8 i − 5 j + 8 k r A D = 5 i − 8 j + 8 k a) correct unit vector for AB? b) correct unit vector for AC? c) correct unit vector for AD?

Use the definition of scalar product, a b = ab cos 0, and the fact that a b = axbx + ayby + a₂b₂ to calculate the angle between the two vectors given by a = 4.01 + 4.0 + 4.0k and b = 4.01 + 7.0 +6.0k. Number i Units

The grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled A⃗ A→ through D⃗ D→. This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. A. What is the xcomponent of A→? B.What is the y component of A⃗ ? C.What is the y component of B⃗ ? D.What is the x component of C⃗ ? E. In ordered pair notation, write down the components of vector B⃗  F. In ordered pair notation, write down the components of vector D G.What is true about B⃗  and D⃗ ? They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors.

5..

CLO 4 If the plane x+y+z-1=0 cuts the x-axis, y-axis, and z-axis at A, B, and C respectively. Find the perpendicular distance to the point P(2,6,9). В а. 9.24 b. 8.66 С. 9.81 d. None of the choices О е. 5.33 f. 5.67 N.

Problem 17. For the tree in Problems 13 and 14. knowing the tension in cable AB 13 950 lbs 1bs and the tension in cable AC is 810 lbs. determine the magnitude and direction of the resultant force atA Write the force vector of the resultant A in terms of its unit vectors. 45° 25 40 P.

Given vectors: A = 8.3i + 3} and B= 6.5i + 7.4) Find AXB O a. 73.00 O b. 76.15 O c. 41.92 O d. 80.92 e. 31.75

Evaluate each of the following. Assume î, ĵ, k are the unit vectors aligne with the x, y, and z axes, respectively. a. î j = d. (4î – j) · (3î + 5j – 10k) = b. k - k= c. k- î=

Elliptical cylindrical (EC) coordinates are defined by the variables u, v and z, with aconstant a, in terms of Cartesian coordinates as follows:x = a cosh u cos v ;y = a sinh u sin v ; (75)z = z .a. Find the EC metric.b. Describe surfaces of constant u, v and z for various values of the constant a.c. Find the EC basis vectors for arbitrary a.d. Make vector field plots of the EC basis vectors in the x-y plane.e. Find the incremental area and volume expressions.f. Express the gradient, divergence, curl and Laplacian operators in EC coordinates.

Consider two vectors, A = 16.5 m at 48.0°, and B = (-12.7 + 2.30j) m. Determine the x and y components of A: Ax Ay m. Determine the x and y components of B: B. Let H- B- 3 A. Determine H and express it in unit vector form. 1+ コ)-H Determine the magnitude and direction of H H= mat 3: