Page 73 - Math SL HB Sem 2

Kolej MARA Seremban Mathematics IB High Level
Core : Vectors

The Angle between Two Straight Lines

Suppose two straight line vector equations are

:11 *fv1
11
12:a2+sV2

With t and s are any scalars and 0 is angle between two straight lines.

:i1 */v1
11
Y2

Vt
12: a2 + svz
e e

If 0 is angle between two straight lines, its also 0 between v1 and v2 . because ofthe lines
are parallel.
vr. v2 =
lv,llvrlcose

- v,.v.
cosu=lv,ii;;

Hence, the angle between two straight lines given by

6 : .vr'vz
"oa-t
In,ll,,l

Two straight lines are perpendicular if v1 . v2:0 and the straight lines are parallel if
:
l v1 tv2 for t scalar.

Example

The vector two straight lines equation are given by
p = (2i+ 2j - 4k + ( i+ 3j - 3k)
)
and q: ( i+j + k) +s( i + 2j - 4k)

with t and s scalar. Find the acute angle between that two straight lines.

Answer : o : cos-1(0.951) r 18.
l