If projection of any line on coordinate axes 3, 4 and 5, then its length is

Question

If projection of any line on coordinate axes 3, 4 and 5, then its length is (A) 12 (B) 50 (C) 5 √2 (D) 3 √2

Tardigrade Admin · Accepted Answer

Let d be the length of line, then projection on x-axis =d l=3, projection on y axis = dm =4 and projection on z-axis = dn =5 Now, d 2( l 2+ m 2+ n 2)=50 ⇒ d2=50 ⇒ d=5 √2

Q. If projection of any line on coordinate axes $3, 4$ and $5$ , then its length is

$12$

$50$

$52$

$32$

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

Q. If projection of any line on coordinate axes 3,4 and 5, then its length is

12

50

52​

32​