Dot product and cross product evaluation questions

[thomas49th]

This question has a few parts.

r = i + 2j + 3k
s = 2i - 2j - 5k
t = i - 3j - k

Evaluate:

a)(r.t)s - (s.t)r
b)(r x s) x t.

deduce that (r.t)s - (s.t)r = (r x s) x t


can you prove this relative true for any three vectors

a)(r.t)s - (s.t)r
(r.t)s

well I don't know what s is doing to inside the bracket. I don't think it's the cross product rule.
Anyhow

(r.t) means use dotty dot product

r.t = |r||t|cos(x)

problem uno. I don't know the angle between the vectors.

Am I just being stupid. I thought about possibly trying to get the angle from the cross product, or using some trig identity but I think that'll be a road to nowhere

Hint?

Thanks
Thomas

 

[sara_87]

hi,

ok, first you need: (a) (r.t)s - (s.t)r

you are given the vectors. For this, you don't need to use the formula:
r.t = |r||t|cos(x)

If you have two vector, do you know how to evaluate the dot/scalar product?

 

[thomas49th]

im being an idiot

r.t = (i - 6j- 3k)

but what operation does the s outside of (r.t)s do?

Thanks

 

[thomas49th]

and I am being an idiot agin, the dot product is scalar and so I'm merely multiplying all values of s by the scalar value returns from r.t

1 - 6 - 3 = -8

so (r.t)s = -8(s)

=> s = 16i - 16j - 40k

Good so far?

 

[sara_87]

ya, good so far :)

now, do the same for (s.t)r

so can you now evaluate (a) (r.t)s - (s.t)r