# Homework 10/5/99

## Chapter 3:

Q6.  When two vectors are added, the magnitude of the sum will be the greatest when the vectors point in the same direction.  In this case the magnitude will be 7.5 km.  When the vectors point in different directions the sum will be smaller.   The sum will be the smallest when the vectors point in exactly opposite directions.   In this case the magnitude of the sum will be 0.5 km.

Q7.  Two vectors must have the same magnitude and point in opposite directions to exactly cancel, that is, to add up to zero.  Three unequal vectors can add up to zero if the two shorter vectors are opposite the longest vector and the sum is zero.   Three unequal vectors can also add up to zero when they form a triangle and the head of the third vector meets the tail of the first vector

Q8.  The magnitude of a vector can equal one of its components when the vector lies along the x or y axis.  If a vector is at an angle to the x or y axis, the component is smaller than the magnitude of the vector.  The component can never be greater than the magnitude of the vector.

Q9.  According to the Pythagorean theorem, the sum of the squares of the components equals the magnitude squared.  When the magnitude squared is zero, all of the components must be zero since they are all positive when squared and cannot cancel one another out.