physics
posted by Eunice .
Two vectors have magnitudes 3.0 and 4.0. How are the directions of the two vectors related given the following conditions?
1) The sum has magnitude 7.0.
(a)They both point in the same direction.
(b)They each point in opposite directions.
(c) They are perpendicular to each other.
2) If the sum has magnitude 5.0.
(a)They both point in the same direction.
(b)They each point in opposite direction.
(c) They are perpendicular to each other.
3) What relationship between the directions gives the smallest magnitude sum?
(a)They both point in the same direction.
(b)They each point in opposite direction.
(c) They are perpendicular to each other.
What is this magnitude?

If you haven't had trig, you can do this using a paper and pencil and a ruler.
1. Draw a horizontal arrow 3.0 inches long, with the arrow head on the right end.
2. Starting at the above arrow's arrowhead, draw another arrow, this time 4.0 inches long, in all 3 possible directions.
3. You are now interested in the total displacement: that is, the length of a line if drawn from the very beginning of the first arrow (the end opposite its arrowhead) to the very end of the second arrow (the tip of its arrowhead).
Now just measure each displacement and answer the questions. 
Forgot to say:
When drawing vectors as arrows, the magnitude is the length of the arrow.
(The second component of a vector is direction.)