Vector B has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of B and (b) the angle that B makes with each coordinate axis.

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 .

The figure shows two displacement vectors A and B. Vector A points at an angle of 22.0° above the x axis and has an unknown magnitude. Vector B has an x component Bx = 32.0 m and has an unknown y component By. These two vectors are equal. Find (a) the magnitude of A and (b) the value of By. B, 22.0° (a) 0 B₂ 32.0 m (b) (a) Number i (b) Number i Ā +X +X Units Units

Vector V1 is 5.0 units long and points along the negative x-axis. Vector V2 is 10.0 units long and points at an angle of 30.0 degrees above the positive x-axis. (a) Find the x and y components of the vector sum V2 + V1 and then determine the magnitude and direction of the vector sum V2+V1. (b) Sketch the vector sum V2+V1 on a grid.

A hiker walks 2.5 miles in a direction 65° West of North, then 3.5 miles in a direction 40° South of West, then 1.5 miles due South. What must be the vector displacement of the hiker during the fourth part of the trip in order for the resultant to be 5.5 miles due West for the entire trip? Drawing a vector diagram or drawing individual vectors will help.

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

Vector A has a magnitude of 5 at an angle of 36.9 counter clockwise from the x-axis. The components Ax and Ay are?

Consider the following vectors: A = 5.2j;  B = -4.1i + 2.5j.  Draw a diagram showing the addition of vectors A and B. (a) Find A + B in the Cartesian (x and y component) form. (b) Find the magnitude of A + B. (c) Find the direction of A + B, expressed as a polar angle. (d) Find 1.5A - 3.2B in the Cartesian (x and y component) form. (e) Find the magnitude of 1.5A - 3.2B. (f) Find the direction of 1.5A - 3.2B, expressed as a polar angle.   Note: New drawing also with solution

Three vectors A, B, and C have the following components: Ax=5.00, Ay=7.00; Bx=4.00, By=3.00; Cx=2.00, Cy=5.00. (a) Find the x and y components of A+B +C. (b) Find the magnitude and direction of A+B+C

Given vectors a=(10,-9) and b=(0,-5) Find the magnitude of the resultant vector: T = 3 a +26