Possible Magnitudes for Resultant Vector

[ThomasMagnus]

Two vectors whose magnitudes are 3.5m and 4.5m, respectively, are added together. Which of the following cannot be the magnitude of the resultant vector.

A) 0.5m
B)1.0m
C)3.5m
D)7.0m


Here's what I tried

2 situations: if the vectors are in the same direction:
3.5m+4.5m=8.0m

If in opposite directions:

3.5+(-4.5)=-1.0--->magnitude is 1.0
(-3.5)+4.5=1.0

Where are 7.0, 3.5, and 0.5 coming from??


Thanks

 

[RTW69]

Solve this problem graphically. Draw a vector 4.5 cm long. Draw another vector 3.5 cm long on another scrap of paper. Lay the tail of the 3.5 cm vector on the head of the 4.5 cm vector so they form a straight line of length 8 cm. The angle between the vectors is 180 degrees. Rotate the 3.5 cm vector around the head of the 4.5 cm vector varying the angle from 180 degrees to 0 degrees. observe the distance from the head of the 3.5 cm vector and the tail of the 4.5 cm vector. You will find all of the above distances but one.

 

[ThomasMagnus]

Aha! Thank you.

I found that the vector length can be anything between 8and1

 

[ThomasMagnus]

then a is the answer?

 

[RTW69]

correct