Question

Question #0796e

Answer 1

The magnitude of the vector is between `1` and `7`.

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 `veca` and `vecb` together, then the range for the new vector's magnitude is:

`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 same direction

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

Using this range, and the fact that `absveca = 3` and `absvecb=4`, we see 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 `1` and `7`.

Final Answer