vectors and linear algebra (1st yr uni) (1 Viewer)

[melimoo]

(also x-posted in usyd)

my trouble:

if i'm given 2 points, say, P(x,y,z) and Q (X,Y,Z) and i want to find the line through them, i assume i use the formula (if wanting parametric vector eqn)
r = ro +tv

now do i take P to be ro and Q to be r, or do i make Q into the parallel vector v ?????? can i even plug in Q(X,Y,Z) to get v? i don't think thats right..... HELP

also,

how about orders of operations concerning dot and cross products?

like say i had a . b x c ?

thanks dears

 

[YBK]

like say i had a . b x c ?

I thought a point meant multiplies... hmmm...

weird... *goes back to chemistry*

 

[darkliight]

Ok, to describe a line in R³ we need two things, 1. a point on the line (r₀) and 2. a vector parallel to the line (v).

1. is easy, we're given two points to choose from so just pick one.
For 2. just remember the vector PQ is parallel to this line (and remember this vector is just < X-x, Y-y, Z-z >).

so r = < x,y,z > + t< X-x, Y-y, Z-z >

As for the order of operations, you must do the cross product first. Remember, a x b is a vector, but a . b is a scalar.

In your example of a . b x c, if we do a . b first, we get some scalar, s, then s x c doesn't make sense So yeah, cross product first (because that makes sense and we get another vector) and then the dot product (which again makes sense).

Hope that helps.

 

[melimoo]

Ok, to describe a line in R³ we need two things, 1. a point on the line (r₀) and 2. a vector parallel to the line (v).

1. is easy, we're given two points to choose from so just pick one.
For 2. just remember the vector PQ is parallel to this line (and remember this vector is just < X-x, Y-y, Z-z >).

so r = < x,y,z > + t< X-x, Y-y, Z-z >

As for the order of operations, you must do the cross product first. Remember, a x b is a vector, but a . b is a scalar.

In your example of a . b x c, if we do a . b first, we get some scalar, s, then s x c doesn't make sense So yeah, cross product first (because that makes sense and we get another vector) and then the dot product (which again makes sense).

Hope that helps.

omg
thankyou
thats so simple
i wish i could send you e-flowers or chocolates.
why can't my lecturers/tutors explain it like that. ARGH

THANKYOU