The projection of any line on coordinate axes be respectively 3, 4, 5, then its length is:

Question

The projection of any line on coordinate axes be respectively 3, 4, 5, then its length is: (A)  12  (B)  50  (C)  5√2  (D) none of these

Tardigrade Admin · Accepted Answer

Let d be the length of line, then projection on x-axis = dl = 3, projection of y-axis = dm = 4 and projection on z-axis = dn = 5 d2(l2+m2+n2)=50 ⇒ d2=50 ⇒ d=5 √2

Q. The projection of any line on coordinate axes be respectively $3, 4, 5,$ then its length is:

$12$

$50$

$52$

none of these

Let $d$ be the length of line, then projection on $x$ -axis $= d l = 3$ ,
projection of $y$ -axis $= d m = 4$
and projection on $z$ -axis $= d n = 5$
$d^{2} (l^{2} + m^{2} + n^{2}) = 50$
$\Rightarrow d^{2} = 50$
$\Rightarrow d = 52$

Q. The projection of any line on coordinate axes be respectively 3,4,5, then its length is:

12

50

52​