Page 75 - Math SL HB Sem 2

Kolej MARn Seremban Mathematics IB High Level
Core : Vectors

Line t has equationsr =-1 +2s,y=l-2s utdz:l + 4s.
Line 2 has equationsr: 1 t ,y: t and,z:3 2t.
v I z
-
Line 3 has equations ::---- =- v -l=' -A' .
'2'3
a) Show that line 1 and line 2 are parallel.
b) Show that line 2 and line 3 intersect and find the angle between them.

a) Line t has direction vector 2i-2j + 4k = 2(i j + 2k)
-
Line 2 has direction vector-i + j 2k = (i j + 2k)
-
- -
-
.'. both line I and line 2 are parallel to i j + 2k and so mwt be parallel to each other.
b) Substituting line 2's equations into line 3's, gives

l-r-1 7-)t-L
23

.. the lines intersect att:-2,i.e at(3,-2,7).

lr=-i+j-2k

e
13=2i-j+3k
r-1 - y-l z-4

2 1 J

x-1 y+l z-4
2-r3
...t3:2i-j+3k

The acute angle between lines 2 and 3 is found
using
t,'t,
I
cos, = I
lr,llr,l

e:
"o.-r7--2-)*to.te"