Consider the three displacement vectors A = (4î - 3ĵ) m, B = (6î - 7ĵ) m, and C = (-81 + 5ĵ) m. Use the component method to determine the following. (Take the +x direction to be to the right.) (a) the magnitude and direction of the vector D = A + B + C X magnitude Note that all three vectors lie in the xy plane so the sum of these vectors will also lie in the xy plane. mi x The angle you give does not put the sum into the correct quadrant.° counterclockwise from the +x axis direction (b) the magnitude and direction of E= -A-B+C magnitude m direction ° counterclockwise from the +x axis

Assuming the +x-axis is horizontal and points to the right, resolve the vectors given in the following figure to their scalar components and express them in vector component form. yA 1. 60° A = 10.4 30° 30° 20.2 6 D = 20.2 53 37° A = В - F = C = 12.4 B = 5.4

The vector B⃗ is added to a vector C⃗ given as C⃗ = −3i ^ + j ^. The resultant vector obtained as a result of this process is R⃗ = B⃗ + C⃗. The resultant vector is in the positive y direction and the size of this vector is equal to the size of the B⃗ vector (| R⃗ | = | B⃗ |). According to what is given; a-) What is the size of the B⃗ vector? b-) What is the angle between the vector B⃗ and the vector C⃗?

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.

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?

The magnitude of Ais 5.7. Vector Alies in the second quadrant and forms an angle of 23 degrees with the y- axis. The components, Ax and Ay, are closest to: O Ax = -5.2, Ay = -2.2 O Ax=+5.2, A, = -2.2 Ay O Ax = -5.2, Ay = +2.2 O Ax = +2.2, Ay = -5.2 O Ax = -2.2, Ay = +5.2