LQ1 Phys 111 Spring 1999
 

Given two vectors: = 1i + 4j  ,   = -4i + 8j

1). The resultant vector C obtained by adding together the both vectors has the magnitude and makes an angle with (positive) x axis :
A) 11.9, 32.40              B) 18.6, 1360                    C) 7.4, -470                  D) 144, -750                 E) 12.4, 1040

2). The result of dot product  is:

A) 85            B)  115            C) 139             D) 206               E) 233

3). The angle (in degrees) between the two vectors A and B is:

A) 40.6         B) 56.3            C) 86.8             D) 113.6            E) 127.5
 

Adding vectors means adding components
Vector (-3,+12) is in the second quarter as can be seen from its components.  The angle must be then in between 900 and 1800
Find first A+2B  and A-B  in the component (unit vector) form then find dot product by multiplying x components, multiplying y components and summing the results of both products.
 
 

1E       2B      3A