vector addition
<3,5> + <9,2>
What is <12,7>
<3+9,5+2> = <12,7>
<3,2> - <7,1>
What is <-4,1>
<3-7,2-1>=<-4,1>
<3,9>
What is √90 or 9.487
√(3)2+(9)2=√9+81=√90
<4,7>
What is 60.251 degrees
tan-1(7/4)
<6,2>
What is √40 (or 6.325) and 18.4349 degrees.
√(6)2+(2)2=√40
tan-1(2/6)=18.4349
<-7,22>+<3,-10>
What is <-4,12>
<-7+3,22+(-10)>=<-4,12>
<-13,12> - <12,-2>
What is <-25,14>
<-13-12,12+2>=<-25,14>
<6,6>
What is √72 or 8.485
√(6)2+(6)2=√36+36=√72
<9,3>
What is 18.4349 degrees
tan-1(3/9)
<18,5>
What is √349 (or 18.682) and 15.5241 degrees
√(18)2+(5)2=√349
tan-1(5/18)=15.5241
<3.15,9>+<-4,4.5>
What is <-0.85,13.5>
<3.15+(-4),9+4.5>=<-0.85,13.5>
<6.25,3.99> - <6,-3>
What is <0.25,6.99>
<6.25-6,3.99+3>=<0.25,6.99>
<3.5,9>
What is √93.25 or 9.657
√(3.5)2+(9)2=√12.25+81=√93.25
<3.19,5>
What is 57.4621 degrees
tan-1(5/3.19)
<-7,6>
What is √85 or 9.220 and 139.399 degrees
√(-7)2+(6)2=√85
180 - tan-1(6/-7)= 139.399 degrees
Vector u:
Magnitude: 10 , Direction Angle: 45 degrees.
Vector v:
Magnitude: 20, Direction Angle 135 degrees.
Find u+v in component form.
What is
<-5sqrt(2)/2 , 15sqrt(2)/2>
or
<-3.536 , 10.607>
(4i-3j)-(2i+4j)
What is (2i-7j)
((4i-2i)+(-3j-4j))=(2i-7j)
<1.25,12.63>
What is √161.0794 or 12.692
√(1.25)2+(12.63)2=√1.5625+159.5169= √161.0794
<-6,5>
What is 140.194 degrees
180 - tan-1(5/6) = 140.194 degrees
<4.82,3>
What is √32.2324 (or 5.677) and 31.8984 degrees
√(4.82)2+(3)2=√32.2324
tan-1(3/4.82)=31.8984
<-5, 2>+<3, -3.5>
Find the magnitude and direction of the resultant.
What is
Magnitude: 2.5
Direction: arctan(1.5/2) + 180 = 216.870
(3i-3.4j)-(4j+2i)
What is (i-7.4j)
((3i-2i)+(-3.4j-4j))
<0.1,0.3>
What is √0.1 or 0.316
√(0.1)2+(0.3)2= √0.01+0.09=√0.1
<9.23,-2.2>
What is -13.4065 degrees (or 346.5935 degrees)
360 - tan-1(2.2/9.23) = 346.5935 degrees
<-9.32,6.8>
What is √133.1024 (or 11.537) and 216.115 degrees
√(-9.32)2+(6.8)2=√133.1024
180 + tan-1(6.8/9.32)=216.115