Begin2.DVI

I6-20.

(d) (~r−~r 1 )·N~= 0

is equation of plane

I6-21. T~=ˆe 1 −ˆe 2 is tangent to line. x= 3 +λ, y= 4−λ, z= 2

I6-22.
N~ =12ˆe 1 − 16 ˆe 2 + 12ˆe 3
Equation of plane is
(~r−r 1 )·N~= 0
or3(x−4)−4(y−3) +z= 0

I6-23.

Plane throughP 0 P 1 and perpendicular toN~
and plane throughP 2 P 3 also perpendicular toN~
are parallel planes.
The vectorP 2 P 1 is vector from one plane
to the other and its projection ontoN~ is distance between planes
and also equal to the minimum distance between the skew lines.
I6-24. x= 1+2t, y= 5t, z= 1+2tis parametric equation of line. The point(6, 13 ,12)

is not on the line.

I6-25. If~r−~r 1 is colinear with(~r 2 −~r 1 ), then(~r−~r 1 )×(~r 2 −~r 1 ) =~ 0 By vector addition

~r=~r 1 +λ(~r 2 −~r 1 )whereλis a parameter.

I6-27.

i= 1, j= 2, k= 3, ˆe 1 ׈e 2 =ˆe 3

even permutations i= 2, j= 3, k= 1, ˆe 2 ׈e 3 =ˆe 1

i= 3, j= 1, k= 2, ˆe 3 ׈e 1 =ˆe 2

i= 3, j= 2, k= 1, ˆe 3 ׈e 2 =−ˆe 1

odd permutations i= 2, j= 1, k= 3, ˆe 2 ׈e 1 =−ˆe 3

i= 1, j= 3, k= 2, ˆe 1 ׈e 3 =−ˆe 2

Solutions Chapter 6