Page 69 - Math SL HB Sem 2

Kolej MARA Seremban Mathematics IB High Level
Core : Veclors

Vector Arithmetic

Vectors in space apply the sarne rules of addition , subtraction, scalar multiplication and
also the magnitude just as they are in the plane.

For any vectors v1:a1i+D1j+c1k arld y2=a2i+ bzi + c zk , and for any scalar t,

2 -2 2
A)l Vt at +q +cl

|
B) vr + v2: (a1+ a2)i+ (b + b 2)i + (c 1+ c2)k
vl -v2:(a1 - a2)i+ (b r - )i+(c1 - c2)k
b

+
C) ktt 1 = ka 1i + kb 1i kc 1k
Example
fina lZa-Ul where a:i+j+k and b=-i+3j-2k.

:
2a b 2(i + j + k) (-i + 3j 2k)
-
-
-

lza-ul: lri-1++t l

J%

Example

Find a unit vector u in the direction of the vector from A(l , 0 , 1) to B(3 ,2 ,0). Hence,
find a vector 6 z nits long in thal direction.

-+ -)
AB =- o" OA AB 22 +22 +(-l)2

-+
AB _ 2i+2j-k : ?i*?i 1k
u
frt 3 J.'J

-+
AB :6 2 ) 1 :4i+4i-2k
The vector we want is 6 l I + t J k
Hi 3