EXERCISES PROBLEMS VECTOR
15E. Vector has a magnitude of 5.0 m and is directed east. Vector b has a magnitude of 4.0 m and is directed 35 west of north. What are (a) the magnitude and (b) the direction of b? What are (c) the magnitude and (d) the direction of b o? (e) Draw a vector diagram for each combination.
16E. For the vectors give 0 b in (a) unit-vector notation. and as (b) a magnitude and (c) an angle (relative to ). Now give b in (d) unit vector notation. and as (e) a magnitude and (f) an angle.
17E. Two vectors are given by In unit vector notation. find (a) , (b) , and (c) a third vector c such that b + c = O.
18P. Here are two vectors What are (a) the magnitude and (b) the angle (relative )? What are (c) the magnitude and (d) the angle of b?
19P. Three vectors , b and c each have a magnitude of 50 an plane. Their directions relative to the positive direction of the x axis are respectively.
20P. What is the sum of the following four vectors in (a) unit vector notation and (b) magnitude-angle notation?
21P. The two vectors 0 and b have equal magnitudes of 10.0 m. Find (a) the x component and (b) the y component of their vector sum. (c) the magnitude of T, and (d) the angle makes with the positive direction of the x axis.
22P. In the sum it B C, vector it has a magnitude of 12.0 m and is angled 40.0 counterclockwise from the x direction, and vector C has a magnitude.
23P. Prove that two vectors must have equal magnitudes if their sum is perpendicular to their difference .
24P. Find the sum of the following four vectors in (a) unit vector notation, and as (b) a magnitude and (c) an angle relative to x.
25P. Two vectors of magnitudes a and b make an angle 8 with each other when placed tail to tail. Prove, by taking components along two perpendicular .
26P. What is the sum of the following four vectors in (a) unit vector notation, and as (b) a magnitude and (c) an angle?
27P. (a) Using unit vectors, write expressions for the four body diagonals (the straight lines from one comer to another through the center) of a cube in terms of its edges which have length.
Vectors and the Laws of Physics :
28E_ A has the magnitude 12.0 m and is angled 60.0 counterclockwise from the positive direction of the x axis of an coordinate system.
29E. A vector 0 of magnitude 10 units and another vector b of magnitude 6.0 units differ in directions by 60°.
30E. Derive for a scalar product in unit vector notation.
31P. Use the definition of scalar product b = ab cos 8, and the fact that calculate the angle between the two vectors.
32P. Derive for a vector product in unit vector notation.
33P. Show that the area of the triangle contained between 0 and band the red line.
34P. In the product F = B, take q = 2, v = o + 4.0 + 6.0 and F = 4.01 + 12 k. What then is B in unit vector notation.
35P. (a) Show that o (b) is zero for all vectors 0 and b. (b) What is the magnitude of 0 x (b) if there is an angle c between the directions of a and b.
37P. The three vectors in have magnitudes a = 3.00 m, b = 4.0, and c = 0.0 m. What are (a) the x component and (b) the y component of 0.
38P. There are two vectors in the plane that perpendicular to a and have a magnitude of 5.0 m. One, vector c, has a positive x component and the other,vector d, a negative x component. What are (b) the x component and (c) the y component of c, and (d) the x component and (e) the y component vector of d.