Question

Consider the two vectors A(with arrow above)=5i-3j and B(with arrow above)=-i-2j

1. Calculate A (with arrow above) + B (with arrow above)
2. Calculate A (with arrow above) - B (with arrow above)
3. Calculate absolute value of A (with arrow above) + B (with arrow above)
4. Calculate absolute value of A (with arrow above) - B (with arrow above)
5. Calculate the directions of A (with arrow above) + B (with arrow above) and A (with arrow above) - B (with arrow above).
(answers are counterclockwise from the +xaxis)

Answer 1

i know numbers 1-4..i just dont know question 5..please help!

Answer 2

COUNTER CLOCKWISE MEANS ANTI-CLOCKWISE

Answer 3

i know that..but i dont know how to do that direction

Answer 4

i just dont get number 5 =( i got everything else right

Answer 5

take the inverse tangent to get the angle

Answer 6

what is A + B?

Answer 7

I MEAN
-6I+J

Answer 8

really?

Answer 9

hold on. unless i am very confused
\[5i-3j+(-i-2j)=4i-5j\] correct me if i am wrong

Answer 10

you are right

Answer 11

then a-b is 6i-j

then for the absolute values i got \[\sqrt{41}\] and \[\sqrt{35}\]

Answer 12

so to do the directions...i have to do what exactly?

Answer 13

you want that angle
to find it you see that
\[\tan(\theta)=-\frac{5}{4}\] so
\[\theta =\tan^{-1}(-\frac{5}{4})\]

Answer 14

that will give you a negative number. if that annoys you subtract it form 360 to get the positive coterminal angle

Answer 15

idk what it wants...but thats exactly what it says..i copied the exact question

Answer 16

assuming you are working in degrees. yes?

Answer 17

you need a calculator. make sure it is in degree mode and hit
second - tan - -5/4

Answer 18

so for a+b i got -51.34..so to make it positive i will add 360..right?

Answer 19

yes

Answer 20

i got 308.66

Answer 21

i get -51.34 so if you subtract from 360 you get what you wrote

Answer 22

so the next one will be arc tan of -1/6??

Answer 23

rather "add to 360"

Answer 24

yea when i added i got 308.66

Answer 25

yes the next one would be arctan(-1/6)

Answer 26

+360

Answer 27

350.54?

Answer 28

so it says i got absolute value of a-b wrong

Answer 29

but everything else is right lol

Answer 30

really? why isn't it
\[\sqrt{37}\]?

Answer 31

i got \[\sqrt{35}\]

Answer 32

i added wrong =( lol sorry ill try 37

Answer 33

yeah it is 36 + 1 not 36 - 1

Answer 34

thanks!! =) got it all right!..now onto the next question! thanks again!

Answer 35

A =<5,-3> and B = <-1,-2>

1. Calculate A + B

A = <5,-3>
+B = <-1,-2>
------------
<4,-5>

2. Calculate A - B

A = <5,-3>
-B = <-1,-2>
------------
<6,-1>

3. Calculate |A + B|

sqrt(4^2 + 5^2) = sqrt(16+25)
= sqrt (41)

4. Calculate |A - B|

sqrt(6^2 + 1^2) = sqrt(36+1)
= sqrt (37)

5. Calculate the directions of A+B and A-B.

A+B = <4,-5>

pi + tan-1(-5/4)

A-B = <6,-1>

2pi - tan-1(-1/6)

Answer 36

just for practice :)