Question

Given the vector of AB as shown, draw a vector whose magnitude is half that of AB and in the opposite direction.

Answer 1

whats the question

Answer 2

My answer is AB (arrow above) = -1/2CD (arrow above) but the back of my textbook says it's AB (arrow above) = -2CD (arrow above).. why and how?

Answer 3

your drawing is correct

Answer 4

the length of vector AB is twice the length of vector CD - agreed?

Answer 5

agree

Answer 6

and it is in the opposite direction to CD - agreed?

Answer 7

agree

Answer 8

therefore: AB = -2CD

Answer 9

... but doesn't that look like CD is doubled? o.O

Answer 10

no - lets say CD had a length of 3, then AB would have a length of 6.
therefore 6 = 2 * 3
therefore AB = -2 * CD

Answer 11

I am so confused D:

Answer 12

the question states that CD is half the size of AB,
so you could also write this as:

CD = -0.5 * AB

Answer 13

ohh.. but how about with the answer you mentioned earlier? How did you know?

Answer 14

how did I know what?

Answer 15

these two answers are equivalent:\[\bar{AB}=-2\bar{CD}\]\[\bar{CD}=-\frac{\bar{AB}}{2}\]

Answer 16

about AB = 2CD and wait why is it -0.5*AB and not placed on CD?

Answer 17

ohh okay so I get the CD = -AB/2 but how about the other answer?

Answer 18

if I tell you that I have a number whose value is 6 and ask you to find another number whose value is half my numbers value - what answer would you give?

Answer 19

3

Answer 20

correct, so we can either say that:\[6 = 2\times3\]or:\[3=\frac{6}{2}\]the two statements are equivalent

Answer 21

another way to see this is as follows:

you agree that: CD = -AB/2
now multiply both sides by 2: 2 * CD = -AB/2 * 2 = -AB
now multiply both sides by -1: -2 * CD = AB
swap sides: AB = -2 * CD

Answer 22

alright so how will that connect to AB = 2*CD --> AB = -2CD, CD = AB/2... oohhh!!

Answer 23

thank you! :D

Answer 24

yw :)