5. The first drawing shows three displacement vectors, Ā, B, and C, which are added in a tail-to-head fashion. The resultant vector is labeled R. Which of the following drawings shows the correct resultant vector for A + B - Č? (a) 1 (b) 2 (c) 3 B' R A R R R (1) (2) (3)

Vector A has a negative x component 3.05 units in length and a positive y component 1.95 units in length. (a) Determine an expression for A in unit-vector notation. (b) Determine the magnitude and direction of A. (c) What vector B, when added to vector A, gives a resultant vector with no x component and a negative y component 3.63 units in length? Step 1 The component description determines the unit-vector expression for vector A. Its magnitude and direction are determined from its components. The vector B will be determined from the description of the resultant vector R along with the known components of A. Step 3 (a) We are given Ax A = A Step 2 Determine the unit-vector notation for A using its given components. We know the components of the resulting vector R = A + B, and from this we can determine the vector B A Axî + A,ĵ = (-3.05 = -3.05 = = € -3.05 0 Step 4 (b) The magnitude of A is given by the following equation. 2 A₂²2² + Ay² X X 1.95 -3.05 unit(s) and Ay = 1.95 -3.05 +1.95…

The displacement vector from your house to the library is 590 mm long, pointing 25 ⁰⁰ north of east. What are the x-component (x-axis is directed from west to east) of this displacement vector? What are the y◆-component (y-axis is directed from south to north) of this displacement vector?

Problem 3: Vector A has magnitude 8 and angle 29°. Vector B has magnitude 13 and angle 111°. Part (a) What is the magnitude of the resultant vector? Numeric : A numeric value is expected and not an expression. r =

SS 1. A vector A has a magnitude of 54.0 m and points in a direction 26.0° above the positive x axis. A second vector, B, has a magnitude of 88.0 m and points in a direction 59.0° above the positive x axis. Using the component method of vector addition, find the of the vector C = Ã + B. m Sispargnitudin f60 sst ssf60 ss + ssf60comp 0 ssf60 ssion

A displacement vector in the xy plane is 48.0 m long and directed at angle = 35.0° in the figure. Determine (a) the component and (b) the y component of the vector. Ensure you state the correct units.

Vector C has a magnitude of 25.8 m and points in the -y- direction. Vectors A and B both have positive y-components, and make angles of a = 41.4° and ß = 26.7° with the positive and negative x-axis, respectively. If the vector sum A+B+C = 0, what are the magnitudes of A and B? |A| = |B| = m m B A Figure is not to scale.

Problem 1: A displacement vector points in a direction of e = 21° left of the positive y- axis. The magnitude of this vector is D = 105 m. Refer to the figure. Part (a) Enter an expression for the x-component vector, D,, in terms of D, 0, and the unit vectors i and j. D, = cos(a) cos(o) cos(0) cos(90+0) 7 8 HOME sin(a) sin(o) sin(0) 4 5 6. i 1 2 3 k D + END h P t ВАCKSPACE DEL CLEAR Submit I give up! Hint Feedback Part (b) Enter an expression for the y-component vector, D, in terms of D, 0, and the unit vectors i and j. Part (c) Enter an expression for the vector D in terms of D, 0, and the unit vectors i and j. Part (d) What is the sum of the magnitudes of vectors D, and D,., in meters?

With the given three vector A, B, C. Determine the negative vector B. A= 2i - 3j + 4k B= -3i - 6j + 5k C= 4i + 2j

Three displacement vectors of a croquet ball are shown in the figure, where |ÃI = 25.0 units, IBI 45.0 units, and ICI = 40.0 units. W 0 Need Help? B 45.0° 45.0⁰ (a) Find the resultant in unit-vector notation. Read It d (b) Find the magnitude and direction of the resultant displacement. units (from the +x axis)