Question

List I	List II
1) d.c's of $x-$ axis	a) $(1,1,1)$
2) d.c's of $y-$ axis	b)$\left(\frac{]}{\sqrt{3}}\frac{]}{\sqrt{3}},\frac{]}{\sqrt{3}}\right)$
3) d.c's of $z-$ axis	c) $(1,0,0)$
4) d.c's of a line makes equal angles with axes	d) $(0,1,0)$
	e) $(0,0,1)$

The correct order for 1, 2, 3, 4 is

• A. $c,d,e,b$
• B. $a,b,c,e$
• C. $c,d,a,b$
• D. $b,c,a,e$

Answer 1

The correct option is A $c,d,e,b$

On the $x-$ axis, the other $2$ coordinates $y,z$ will be $0$.

So, the point is $(1,0,0)$

Direction cosines of $x-$ axis i.e $(1,0,0)$ is $(1,0,0)$

$\therefore$ Direction cosines of $x-$ axis are $(1,0,0)$

Similarly, direction cosines of $y$ and $z$ axes are $(0,1,0)$ and $(0,0,1)$ respectively.

$⟹1\to c,2\to d,3\to e$
For the fourth part where we need to find the dc's of a line that makes equal angles with the axes.
The components of such a line will always be equal.
Moreover, the sum of the squares of the dc's of a line should be equal.

If the point is $(a,a,a)$, then $a^2+a^2+a^2=3a^2$

So, the direction cosines are $(\frac{a}{\sqrt{3a^2}},\frac{a}{\sqrt{3a^2}},\frac{a}{\sqrt{3a^2}})=(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}})$

$⟹4\to b$

Hence, option A is correct.