Can you find two vectors with different lengths that have a vector sum of zero?

Answer 1

If you had a vector, we can separate it into its component so we can easily see the result.

Doing the process to two vectors, we can find their respective components. Let's call the 2 vectors A and B.

then the components are Ax, Ay, Az, Bx, By, Bz.

Then we for the 2 vectors to cancel, then each corresponding component must also cancel out, i.e.

Ax + Bx = 0, and so forth Implying that

Ax = -Bx and so forth.

Finally impying that A and B are exact opposites, meaning they have the same magnitude (length) and opposing directions.

So, in a nutshell, the answer is NO.

However, we can find at least 3 vector that will satisfy your question.

Answer 2

Nope...

Imagine drawing vectors.

Draw one random vector (start at origin for simplicity)

The only other vector you can add to it to get to the point you started from is the exact same vector but flipped up down and left right. This vector MUST HAVE the same length!

-T

Answer 3

I think they can't exist...

Think of a one dimensional vector: you can sum only two vectors with the same length and opposite signs to obtain a vector sum of zero. The same is for multi-dimensional vectors too.

Answer 4

u just gotta find the components of the vectors, and those components (be it x and y or x and y and z) should cancel each other out
simple
but, requires a lil brain work
:)

Answer 5

Nope.