Question

The direction cosines of a vector r which is equally inclined to ox,oy and oz. If modulus of r is given,the total number of such vectors is given by

Answer 1

Answer:

Let l,m,n be the direction cosines of

r

.

Since

r

is equally inclined with x,y and z-axis, l=m=n

∴l

2

+m

2

+n

2

=1

⇒3l

2

=1

⇒l=±

3

1

∴ direction cosines of

r

are ±

3

1

,±

3

1

,±

3

1

Now,

r

=

∣

∣

∣

∣

r

∣

∣

∣

∣

(l

i

^

+m

k

^

+n

k

^

)⇒

r

=

∣

∣

∣

∣

r

∣

∣

∣

∣

(±

3

1

i

^

±

3

1

j

^

±

3

1

k

^

)

Since + and − signs can be arranged at three places, there are eight vectors, i.e.,2×2×2 which are equally inclined to axes.