A vector  A  has components  Ax = −6.50 m  and  Ay = 8.50 m.  Find the magnitude (in m) and the direction (in degrees counterclockwise from the +x-axis) of the vector.

Vector Á has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors make an angle of 50.0° with each other. Find Á · B.

Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let  be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let  be the displacement vector with a magnitude of two meters due northwest. Express vectors  and  in unit vector component form.  =    =   The net displacement is given by the vector sum:   =   By Pythagorean theorem,the magnitude of the displacement is:  =  meters. The direction of the resultant displacement is: -- north of east.

Vector C has a magnitude of 22.2 m and points in the −y‑ direction. Vectors A and B both have positive y‑ components, and make angles of α=42.4 and β=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 sailboat race course consists of four legs, defined by the displacement vectors ABC, and, as the drawing indicates. The magnitudes of the first three vectors are A = 2.70 km, B-5.30 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 (b) Number Units Units B Finish- K 35.0 X 40.0⁰ Start

Two vectors are given by a = 9.71 + 4.6) and = 9.21 + 9.5). Find (a) đ x b) .( +) and (d) the component of a along the direction of b ? (a) Number Units (b) Number Units (c) Number Units (d) Number Units

Vector A has components Ax=−8.20 and Ay=11.7 . What is the magnitude A of this vector? ?=? Determine the angle θ in degrees between the calculated vector and the +x‑axis, measured counterclockwise from the +x-axis. ?=?

Two vectors, r and s lie in the xy plane. Their magnitudes are 4.58 and 8.82 units, respectively, and their directions are 304° and 76.0°, respectively, as measured counterclockwise from the positive x axis. What are the values of (a) r and (b) T x 3? (a) Number i -27.03 Units (b) Number i 30.02 Units

Vector A has a magnitude of 34 units and points in the positive y-direction. When vector B is added to A, the resultant vector  A+B  points in the negative y-direction with a magnitude of 18 units. Find the magnitude of B?

The route followed by a hiker consists of three displacement vectors A,B ,c Cand . Vector  A is along a measured trail and is 1550 m in a direction 25.0° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0° east of south. Similarly, the direction of vector C is 10.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or  A+  B+ C = 0. Find the magnitudes of vector B and vector C .