Is it true that $left(vec w-dfrac12vec uright)perpleft(2vec w-vec uright);forallvec u,vec w$?
Clash Royale CLAN TAG#URR8PPP
up vote
2
down vote
favorite
True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.
I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$
Is it correct?
Thanks!
linear-algebra vectors
add a comment |Â
up vote
2
down vote
favorite
True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.
I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$
Is it correct?
Thanks!
linear-algebra vectors
1
Yes, you are correct.
â saulspatz
Aug 17 at 2:37
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.
I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$
Is it correct?
Thanks!
linear-algebra vectors
True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.
I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$
Is it correct?
Thanks!
linear-algebra vectors
asked Aug 17 at 2:32
manooooh
425214
425214
1
Yes, you are correct.
â saulspatz
Aug 17 at 2:37
add a comment |Â
1
Yes, you are correct.
â saulspatz
Aug 17 at 2:37
1
1
Yes, you are correct.
â saulspatz
Aug 17 at 2:37
Yes, you are correct.
â saulspatz
Aug 17 at 2:37
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
They are parallel
$$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
this shows one is a factor of the another.
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
They are parallel
$$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
this shows one is a factor of the another.
add a comment |Â
up vote
3
down vote
accepted
They are parallel
$$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
this shows one is a factor of the another.
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
They are parallel
$$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
this shows one is a factor of the another.
They are parallel
$$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
this shows one is a factor of the another.
answered Aug 17 at 2:42
Nosrati
20.7k41644
20.7k41644
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2885344%2fis-it-true-that-left-vec-w-dfrac12-vec-u-right-perp-left2-vec-w-vec-u-rig%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
Yes, you are correct.
â saulspatz
Aug 17 at 2:37