Question

vector question

The line l1 passes through the point A whose position vector is 3i+j+2k and is parallel to the vector i+j The line l2 pass the through point B whose position vector is -i-k and is parallel to the vector j+2k . The point P is on l1 and point Q is on l2 and PQ is perpendicular to both l1 and l2 .
FInd the position vector of Q

Answer 1

@amistre64

Answer 2

position vector of Q?

Answer 3

The line l1
passes through the point A whose position vector is 3i+j+2k
and is parallel (has a direction) to the vector i+j

L1:
x=3+1t
y=1+1t
z=2+0t
---------------------------

The line l2
pass the through point B whose position vector is -i-k
and is parallel to the vector j+2k .

L2:
x=-1+0s
y= 0+1s
z=-1+2s
-----------------------

The point P is on l1
point Q is on l2

PQ is perpendicular to both l1 and l2 . cross product

FInd the position vector of Q

Answer 4

the smallest distance between L1 and L2 should define the points of P and Q

Answer 5

In the previous question I find the shortest distance to be 3

Answer 6

when you know the shortest distance, then you need to be able to place it as well