# Question #0796e

##### 1 Answer

The magnitude of the vector is between

#### Explanation:

We don't know the angles that the vectors are at, so we can't find the resultant magnitude.

However, we CAN find a range of possible magnitudes.

If we add two vectors

#abs(abs(veca)-abs(vecb))" " le" " abs(veca+vecb)" " le" " abs(abs(veca)+abs(vecb))#

This notation may look confusing, but just remember that when the || symbols are around a vector, it means **magnitude**, and when they're around a scalar, it means **absolute value**.

So all that this equation is really saying is that the magnitude of the resultant vector must be between:

What you get when the two vectors point in opposite directions

AND

What you get when the two vectors point in the

samedirection

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using this range, and the fact that

#abs(abs(veca)-abs(vecb))" " le" " abs(veca+vecb)" " le" " abs(abs(veca)+abs(vecb))#

#abs(3-4)" " le" " abs(veca+vecb)" " le" " abs(3+4)#

#abs(-1) " "le" " abs(veca+vecb) " "le" " abs7#

#1" " le" " abs(veca+vecb)" " le" " 7#

So we can't determine *exactly* what the vector's magnitude is based on this problem, but we can say for sure that it's between

*Final Answer*