Write direction ratios of the vector a = i + j − 2k and hence calculate its direction
cosines?

Note that direction ratios a, b, c of a vector r = x i + yj + zk are just the respective
components c, y and z of the vector. So, for the given vector, we have a = 1, b=1,
c= –2. Further, if l, m and n the direction cosines of the given vector, then
a
1
b
1
c
2
=
,m =
=
,n =
=−
|r|
|r|
|r|
6
6
6
l=
as | r |= 6
Thus, the direction cosines are
2 ⎞
⎛ 1 1
,
,−
⎜
⎟.
6⎠
⎝ 6 6