In the sum Á + B = Ć ,vector Á has a magnitude of 13.4 m and is angled 35.2° counterclockwise from the +x direction, and has a magnitude of 14.1 m and is angled 13.0° counterclockwise from the -x direction. What are (a) the magnitude and (b) vector the angle (relative to +x) of B ? State your angle as a positive number. (a) Number Units >

Vector A has components Ax = 10.0 and Ay = -14.3. What is the magnitude A of this vector? Determine the angle 0 in degrees between the calculated vector and the +x-axis, measured counterclockwise from the +x-axis.

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 = 3.20 km, B = 5.40 km, and C = 4.40 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. 23.0 (a) Number i (b) Number i Units Units B Finish- + C B 35.0 40.0⁰ - Start

Vector Ä has a magnitude of 10 units and a direction angle of 14° measured counterclockwise from the positive r-axis. Vector B has the same r-component as Ä, but its y-component is 3 times larger. What is the magnitude and direction angle of vector B?

The magnitude of vector A is 40.0 units and points in the direction 335° counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector. Ax= Ay=

In the sum A + B = C, v A has a magnitude of 13.7 m and is angled 49.0° counterclockwise from the +x direction, and vector has a magnitude of 15.8 m and is angled 24.1° counterclockwise from the -x direction. What are (a) the magnitude and (b) the angle (relative to +x) of B? State your angle as a positive number. (a) Number i (b) Number i vector Units Units

A vector A has a magnitude of 7 units and points in the -y-direction, while a vector B has double the magnitude of A and points in the +x-direction. What are the magnitude and direction of the following vectors? Give the directions of each as an angle measured counterclockwise from the +x-direction. (a) A + B magnitude direction (b) A - B magnitude direction (c) B-A magnitude direction unit(s) ° (counterclockwise from the +x-axis) unit(s) ° (counterclockwise from the +x-axis) unit(s) ° (counterclockwise from the +x-axis)

The figure shows three displacement vectors A, B, and C. These vectors are arranged in tail-to-head fashion, and they add together to give a resultant displacement R, which lies along the x axis. Note that vector B is parallel to the x axis. What is (a) the magnitude of vector A and (b) its directional angle 0? +y Ā 0 B 9.00 m R 34.0m (a) Number 25.0m (b) Number i IN c 48.0°/ +x Units 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 = 3.00 km, B = 5.10 km, and C = 4.80 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 IA i (b) Number i Units Units 23.0 7 167 B Finish- B 35.0⁰ A 40.0° Start

The two vectors a and b in the figure have equal magnitudes of 13.3 m and the angles are 0₁ = 25º and 0₂ = 104°. Find (a) the x component and (b) the y component of their vector sum, (c) the magnitude of 7, and (d) the angle makes with the positive direction of the x axis. (a) Number (b) Number (c) Number (d) Number IN 8.8 18.5 20.5 65.7 Units Units Units 0₂ 3 3 m Units °(degrees) x