Q9 of 177 Page 24

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

Let a vector be equally inclined to axes OX, OY, and OZ at angle

Then, the direction cosines of the vector are l = cosα, m = cosα and n = cos α

And, we know that –

l² + m² + n² = 1

cos²α + cos²α + cos²α = 1

3 cos²α = 1

Hence, the direction cosines of the vector which are equally inclined to the axes are

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

ii.

iii.

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

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

Find a vector of magnitude units which makes an angle of and with y and z - axes respectively.