Question

With respect to the origin 0, the points A, B ,C, D have position vectors given by
OA=4i+k, OB=5i-2j-2k, OC= i+j, OD=-i-4k

(i) Calculate the acute angle between the lines AB and CD
(ii) Prove that the lines AB and CD intersect
(iii) The point P has position vectors i+5j+6k. Show that the perpendicular distance from P to the line AB is equal to 3^(1/2).

Answer 1

First one is just dot product over product of magnitudes but I think u would have better luck posting this as a seires of questions rather than lumping altogether like this.

Have u done any of the work yourself_

Answer 2

yeah ok...umm the first part i've been able to attempt it

actually how u would know that two lines intersect?--(ii)

Answer 3

i mean how do you prove it?

Answer 4

Maybe vector equation for the lines and see if they intersect?

Answer 5

Like I said, separate questions will be better.

Answer 6

It will just cause confusion if a lot of people start replying to different parts.

And it is a lot of computations for just 1 person.

Answer 7

(i) Calculate the acute angle between the lines AB and CD
\[\text{ArcCos}\left[\frac{u.v}{|v|*|u|}\right]=\theta \]