Vector(^) calculations
P1^
8
(iv) I
→
J = D
→
E
= −A
→
B
= −p
(v) E
→
F = −B
→
C
= −q
(vi) B
→
E = B
→
C + C
→
D + D
→
E
= q + (q − p) + −p
= 2 q − 2 p
Notice that B
→
E = 2C
→
D.
(vii) A
→
H = A
→
B + B
→
C + C
→
H
= p + q + r
(viii) F
→
I = F
→
E + E
→
J + J
→
I
= q + r + p
Unit vectors
A unit vector is a vector with a magnitude of 1, like i and j. To find the unit
vector in the same direction as a given vector, divide that vector by its magnitude.
Thus the vector 3 i + 5 j (in figure 8.20) has magnitude 3522 += 34 , and so
the vector 3
34
i + 5
34
j is a unit vector. It has magnitude 1.
The unit vector in the direction of vector a is written as â and read as ‘a hat’.
A
A
B C
D
E
C
→
H = B
→
G
F
→
E = B
→
C, E
→
J = B
→
G, J
→
I = A
→
B
Figure 8.20
y
j
2 j
3 j
3 i + 5j
4 j
5 j
O i 2 i 3 i 4 i x
This is the unit vector
3
34
5
34
ij+
Figure 8.19