Q8 of 177 Page 24

Show that the vector is equally inclined with the axes OX, OY and OZ.

Let r⃗ = î + j + k̂

And, |r⃗ | = √ ((1)² + (1)² + (1)²)

= √ 3

Therefore, The direction cosines of the vector r⃗

Now, let α, β and γ be the angles formed by r⃗ with the positive directions of x, y and z axes.

Then,

We have,

Hence, the given vector is equally inclined to axes OX, OY and OZ.

Find the direction cosines of the following vectors :

ii.

iii.

Find the angles at which the following vectors are inclined to each of the coordinate axes :

ii.

iii.

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are

If a unit vector makes an angle with with and an acute angle θ with then find θ and hence, the components of