The two vectors in Fig.3.28 have equal magnitudes of 10.0m and the angles are and . Find the (a) x and (b) y components of their vector sum , (c) the magnitude of , and (d) the anglemakes with the positive direction of the x axis
a) x component of vector sum
b) y component of vector sum
c) Magnitude of vector sum
This problem involves the addition of two vectors and . Using the following relations x and y components of the vector sumcan be found and similarly the magnitude and the angle respectively.
Two vectors and
two angles and
x component of the vector sum r is given by
y component of vector sum is
Using equation (i) the magnitude of vectoris written as
The angle makes with the positive direction of the x axis is
Vector is in the negative direction of a y axis, and vector is in the positive direction of an x axis. What are the directions of (a) and (b) ? What are the magnitudes of products (c) and (d) ? What is the direction of the vector resulting from (e) and (f) ? What is the magnitude of the vector product in (g) part (e) and (h) part (f)? What are the (i) magnitude and (j) direction of ?
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