82. Find the scalar components of three-dimensional vectors Gand H in the following figure and write the vectors in vector component form in terms of the unit vectors of the axes. 60° 45° G = 10.0 145 30° H = 15.0 10

Two vectors have the following magnitude, A = 7.2 m and B = 7.8 m. Their vector product is:  A⨯B = -4.7 m i + 11.4 m k. What is the angle (in degrees) between the vectors A and B? Hint: Use |A⨯B| = AB sin(θ)(please don't round off any number)

You are given 3 vectors: p = j - 3k, q = -2i - j - 3k and r = 4i + j + 3k. You are informed that these three vectors are Cartesian unit vectors. To answer this question, you must use the form:  a1i + a2j + a3k  Find a unit vector in the direction of q

In the cross (or vector) product F = qu x B we know that q = 1 F = −29î + −16ĵ + −18k 6.01 +3.07 + 7.0k V = B = B + BJ + Bi What then is B in unit-vector notation if Bx = By? B = i î+ i Ĵ+ i

Can someone please help me understand this question and how to get the answer? Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum is: 1.) equal to 8.6m 2.) could be as small as 2.0m or as large as 12.0m 3.)is equal to 2m 4. or is equal to 12m. Thank you. I am really confused.

7. Draw the vector fand find the magnitude and direction, counter clockwise from the +r-axis. (a) z=2.5, y=1 (b) ex=-0.5, y=1 (c)₂=-1.5, U-1

12.0 B = 5.0 F = 20.0 86400 365) %3D 24 (6)60) = Esc 60° A = 10.0 30 30° 53° D = 20.0 37° Assuming the +x-axis is horizontal to the right for the vectors in the figure, find the following scalar products. a. Ā . B- b. Č - (- 3) - c. Dx F- a. (5 x F) - ( x Ã) -

1. Let v = -51 + 53 be a vector in R². (a) Find v. (b) Find the angle, 0, in degrees, that v makes with the positive x-axis. (Answer in radians between 0 and 27.) (c) Find a unit vector that points in the same direction as v. Answer in component form.

Problem 4: Vectors A, B, and C are shown in Figure 4. The magnitudes of the three vectors are shown in parenthesis. a. What is the resultant vector R = A + B + C? Answer: R= -3.0î + 3.0ĵ b. What is R, the magnitude of R? Answer: R = 4.2 c. What is 8, the angle R makes with respect to the +x-axis? 0 = 180° - 45.0° B (B= 16.2) Figure 4: Vectors for Problem 4. 68.2° A (A = 10.0) 36.9° = 24.0 C(C=9.8) 135.0⁰ X

The Scalar Product The vectors A andB are given by A = 31 + 1j and B = -1î + 1j. (a) Determine the scalar product A - B. SOLUTION Conceptualize There is no physical system to imagine here. Rather, it is purely a mathematical exercise involving two (vectors Categorize Because we have a definition for the scalar product, we categorize this example as a substitution vy problem. Substitute the specific vector expressions for A and B: A-B = (31 + 1j) - (-1î + 1j) = [3i - (-1)i - [31 - 15 - 13 - (-1) + [1j - 15] The same result is obtained when we use the equation A -B = AB, + A8, + A,B, directly, where A, = 3, A, = 1, B, = -1 and 8, = 1. (b) Find the angle e between A and B. SOLUTION Evaluate the magnitudes of A and B using the Pythagorean theorem: A = VA,? + A, = B = V82 + B 2 = Use the equation A - B = AB cos(e) and the result from part (a) to find the angle (in degrees). cos(e) = AB EXERCISE As a particle moves from the origin to (7i + 5j) m, it is acted upon by a force given by (7î +…