1. ## Proving Vectors 2

A) show geometrically that, for any scalar k and any vectors u and v,
k(u-v)=ku-kv

B) illustrate for k>0 that k(u+v)=ku+kv

Note: bolded are vectors (arrows on top)

ok so these two questions are quite similar.. I think, but I am still having trouble on "proving" them. I am not sure if my method is O.K. (no answers in back of book), so can someone please verify or demonstrate the correct method. Thanks in advance

A) ku-kv=ku-kv
is this ok? does it prove the q?

B) well I thought about this as for any constant number k, it has to be greater than 0 because otherwise the resultant will be 0 and does not prove ku+kv

2. Originally Posted by skeske1234
A) show geometrically that, for any scalar k and any vectors u and v,
k(u-v)=ku-kv

B) illustrate for k>0 that k(u+v)=ku+kv

Note: bolded are vectors (arrows on top)

ok so these two questions are quite similar.. I think, but I am still having trouble on "proving" them. I am not sure if my method is O.K. (no answers in back of book), so can someone please verify or demonstrate the correct method. Thanks in advance

A) ku-kv=ku-kv
is this ok? does it prove the q?

B) well I thought about this as for any constant number k, it has to be greater than 0 because otherwise the resultant will be 0 and does not prove ku+kv
If it's asking you to show something geometrically, it's asking you to draw a picture.

3. ok, ill try to describe my drawings

u and v are vectors |u|=|v|=1
now k(u-v)
not sure how to draw the k part but I drew the (u-v) first
ill describe as a triangle: base is u, v is hypotenuse, (u-v) is height

B) what does it mean by k>0 that k(u+v)=ku+kv
how are u supposed to draw that? doesnt it mean that
ku+kv=ku+kv? im not sure how i would draw these to prove this eqtn

4. Originally Posted by skeske1234
A) show geometrically that, for any scalar k and any vectors u and v,
k(u-v)=ku-kv

B) illustrate for k>0 that k(u+v)=ku+kv

Note: bolded are vectors (arrows on top)

ok so these two questions are quite similar.. I think, but I am still having trouble on "proving" them. I am not sure if my method is O.K. (no answers in back of book), so can someone please verify or demonstrate the correct method. Thanks in advance

A) ku-kv=ku-kv
is this ok? does it prove the q?

B) well I thought about this as for any constant number k, it has to be greater than 0 because otherwise the resultant will be 0 and does not prove ku+kv

To prove A)

Draw two vectors, u and v.

Draw the vector u - v.

Draw a vector parallel to u - v, of a different length (k).

This vector is k(u - v).

Then draw the vectors ku and kv.

Draw the vector ku - kv.

It should be clear that the vectors k(u - v) and ku - kv are parallel and of the same length. Therefore they are equal.

The same process is used to prove B).

5. ok, i think I have part A) thanks,

for part B), what does it mean by k>0..
im not sure how to SHOW k>0 by drawing
like.. does it mean that k must exist, for k>0, or, does it mean that -k (cant go in a diff direction) is not allowed?

so I have:

draw vectors ku and kv
then draw ku+kv vector

k(u+v)
draw vectors u and v, then draw vector (u+v), then beside it (parallel) draw k(u+v) but of diff length.
so now my question is, how do you know about the k>0 does it mean k must exist or does it mean that k cannot be going in a diff direction

6. You are given that k> 0, you don't have to prove it. That means that kv goes in the same direction as v.

,
,

,

,

# vector proof ku in V

Click on a term to search for related topics.