Obtain expressions in component form for the position vectors having the following polar coordinates. (a) 12.0 m, 160° counterclockwise from the +x axis R = m (b) 3.40 cm, 70.0° counterclockwise from the +x axis cm (c) 24.0 in., 212° counterclockwise from the +x axis R = in.

The three vectors in the figure have magnitudes a = 2.80 m, b = 3.00 m, and c = 10.2 m and angle 8 = 26.0°. What are (a) the x component and (b) the y component of a; (c) the x component and (d) the y component of b; and (e) the x component and (f) the y component of ? If = pa + qb, what are the values of (g) p and (h) q? Its X

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

Vector A⃗  has a magnitude of 9.30 m and is pointing in a direction of 25.0 degrees counterclockwise from the positive x axis. Vector B⃗  has a magnitude of 9.70 m and is pointing in a direction of 140. degrees counterclockwise from the positive x axis. What is A⃗ +B⃗ ? Magnitude: Direction (specify as an angle measured counterclockwise from the positive x axis):

Each of the following vectors is given in terms of its x- and y-components. Find the magnitude of vector à and the angle it makes with respect to the positive x-axis, measured counterclockwise, when Ax = 4.00 and Ay = -4.00. A = Find the magnitude of vector B and the angle 0 it makes with respect to the positive x-axis, measured counterclockwise, when Bx = -3.00 and By = 3.00. B = 0A = C = ов = Find the magnitude of vector and the angle 0c it makes with respect to the positive x-axis, measured counterclockwise, when Cx = 0.00 and Cy = -2.00. 0c =

Page 3 of 8 3. Vector A has a magnitude of 13.6 and is at an angle of 30.5° counterclockwise from the +x- axis. Vector B has a magnitude of 25.1 and is -50.3° from the +x-axis. a. Express the vectors in the unit vector notation and b. find the angle between them.

For the vectors in the figure calculate: (a) (AxF)xD=(b) (AxF) x (DxB) (c) (AxF)(DxB)

Problem 2: Given vectors: A = 3 i+j- k, B = - i+ 2j+ 5 k, C = 2 j - 3 k. Find: 1. C. (A + B) 2. Cx (A - B)

The three vectors in the figure have magnitudes a = 3.20 m, b = 3.20 m, and c = 10.2 m and angle e = 43.0°. What are (a) the x component and (b) the y component of á ; (c) the x component and (d) the y component of b; and (e) the x component and (f) the y component of ? If 7 = pd + qb, what are the values of (g) p and (h) q? (a) Number Units (b) Number Units (c) Number |Units (d) Number Units (e) Number Units (f) Number |Units (g) Number Units (h) Number Units

A sailboat race course consists of four legs, defined by the displacement vectors A, B, C, and, as the drawing indicates. The magnitudes of the first three vectors are A = 2.90 km, B = 4.90 km, and C= 5.30 km. The finish line of the course coincides with the starting line. Using the data in the drawing, find (a) the distance of the fourth leg and (b) the angle (. (a) Number i 6.67 (b) Number 21.29 Units Units 0 0 23.0 7 B km + Finish- B 35.0 X 40.0° Start