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Two vectors have magnitude V1= 4 km and V2= 7.5km.  What are the maximum and minimum magnitudes of thier vector sum?

I don't get how to do this, can someone explain it to me?

vector addition rely on direction as well as magnitude; in this question the maximum happens when both vectors are at same angle and same directoin and they add up linearly; thus maximum is 11.5 km. The minimum is when they are at opposite direction and cancel each other out so it is 3.5 km. They can be a whole range of value in between 11.5 and 3.5 given by the formula squareroot(V1^2 + V2^2 - cos(angle)) where angle is the degree between the two vectors when they are added up in a nose to tail fashion. hope this helps.

1.A vector quantity is a quantity which is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity which is fully described by its magnitude.
2.Examples of vector quantities which  include displacement, velocity, acceleration, and force. Each of these quantities are unique in that a full description of the quantity demands that both a magnitude and a direction are listed.
3.Vector quantities are often represented by scaled vector diagrams. Vector diagrams depict a vector by use of an arrow drawn to scale in a specific direction.
4.There are several characteristics of this diagram which make it an appropriately drawn vector diagram.

4.1.A scale is clearly listed
4.2.An arrow (with arrowhead) is drawn in a specified direction; 4.3.Thus, the vector has a head and a tail.
4.4.The magnitude and direction of the vector is clearly labeled.

5.The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow. The arrow is drawn a precise length in accordance with a chosen scale.

6.For more information about this topic you can log onto www.physicsclassroom.com

smart son of a bich is right in the first 1/2 of the answer. But the stuff about a sqrt is wrong.

At first you asked about finding the magnitude of vectors.  Vectors have magnitude and direction. Magnitude is like strength, direction is like north or 30 degrees below horizontal.

The part about V1 and V2 gives you magnitude without giving you direction. So it wants to know what characteristic about the direction part of the vectors will give you max and min vector sum. If both point in the same direction, you get max. If they point in opposite directions the one with less magnitude will cancel part of the magnitude of the larger.

It might help to draw the vectors. Draw one (might as well make it horizontal since the problem doesn't say). It's a line with an arrowhead at one end. Draw the second starting at the arrowhead of the first. Then the vector sum is an arrow starting from the beginning of the first and ending at the arrowhead of the second.

To work your problem, experiment with different directions for the second.

There are other graphic ways to analyse vectors. Some work better in other situations.