Show that the vector is equally inclined to the axes OX, OY, and OZ.
The given vector is a → = i ^ + j ^ + k ^ .
If the direction cosines of the vector are equal, then the vector is equally inclined to OX , OY and OZ .
Magnitude of vector a → is,
| a → | = 1 2 + 1 2 + 1 2 = 3
Direction cosines of a → are ( x | a → | , y | a → | , z | a → | ) .
Here, x = 1 , y = 1 and z = 1 .
Substitute all values for direction cosines, we get,
cos α = 1 3 , cos β = 1 3 , cos γ = 1 3
Since, the direction cosines are equal. Hence, a → is equally inclined to OX , OY and OZ .
The given vector is
If the direction cosines of the vector are equal, then the vector is equally inclined to
Magnitude of vector
Direction cosines of
Here,
Substitute all values for direction cosines, we get,
Since, the direction cosines are equal. Hence,
is
equally inclined to the axes OX, OY, and OZ.