# EXERCISES PROBLEMS VECTOR

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.

Multiplying Vectors

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.