Key(^) points
P1^
8
KEY POINTS
1 A vector quantity has magnitude and direction.
2 A scalar quantity has magnitude only.
3 Vectors are typeset in bold, a or OA, or in the form O
→
A. They are
handwritten either in the underlined form a, or as O
→
A.
4 The length (or modulus or magnitude) of the vector a is written as a or
as | a |.
5 Unit vectors in the x, y and z directions are denoted by i, j and k, respectively.
6 A vector may be specified in
●●magnitude−direction form: (r, θ) (in two dimensions)
●●component form: xi + yj or xy (in two dimensions)
xi + yj + zk or
x
y
z
(in three dimensions).7 The position vector O→
P of a point P is the vector joining the origin to P.
8 The vector A→
B is b − a, where a and b are the position vectors of A and B.
9 The angle between two vectors, a and b, is given by θ incosθ=aa..bb
aabb
where a. b = a 1 b 1 + a 2 b 2 (in two dimensions)
= a 1 b 1 + a 2 b 2 + a 3 b 3 (in three dimensions).