vector misc.

[Bozo]

Let A be the point (-11,3,15) and B the point (10,-4,1). Find the position vector of the point P which divides the line segment from A to B in the ratio 5:2

Confirm the answer is 5/7(21,-7,-14)  ?

Thanks.

[BubbleWrapMan]

That would be vector AP. You need OP, which is OA + AP.

Also, you should probably use i-j-k vectors instead of coordinates.

[Bozo]

Can you confirm what the answer is for me please.

[BubbleWrapMan]

I get 4i - 2j + 5k

[Bozo]

Yeah confirmed.

[Bozo]

Let u,v be an element of R^3 with u dot v=0. Can we conclude that u and v are perpendicular?

[Aurelian]

...*someone's* getting AN to do their Calc 1 assignment for them lololololol

[Bozo]

fk ye, i want my answers confirmed. i've done all the questions

[TrueTears]

Let u,v be an element of R^3 with u dot v=0. Can we conclude that u and v are perpendicular?

correct, although a more formal term to use in higher vector spaces is "orthogonal", but same thing.

[Aurelian]

Let u,v be an element of R^3 with u dot v=0. Can we conclude that u and v are perpendicular?

correct, although a more formal term to use in higher vector spaces is "orthogonal", but same thing.

I don't believe this is correct, as either or both of u and v could be the zero vector (it is unspecified).

[Bozo]

Questioning TrueTears, your treading in shark infested waters my friend....

But yeah you're right lol, its an ambiguous question me and him already discussed what you just said.

[TrueTears]

yeah i discussed this with bozo, i assumed we weren't talking about the trivial case here, but yeah answer the question in 2 parts

[Bozo]

Another vectors question.

u=(-2,2,5) v=(4,3,0) in R^3

The angle between these two vectors is obtuse right, how would i go about sketching the vector projection of v in the direction of u and the vector projection of u in the direction perpendicular to v.


Also, if it asks me to calculate the vector projection of v in the direction of u is that v onto u or u onto v.


thanks.

[brightsky]

u.v = -8 + 6 = sqrt(4 + 4 + 25) sqrt(16 + 9) cos (t)
-2 = 5sqrt(33) cos(t)
cos(t) = -2/(5sqrt(33))
so yes t is obtuse

refer to attached image for the visual representation of vector projections/resolutes. the red line that runs parallel to vector b is the vector projection of a in the direction (or onto) b. the red line that runs perpendicular to vector b is the vector projection of a perpendicular to b.

i think that should answer both of your questions regarding vector projections.