If the foot of perpendicular drawn from the point (2,5 , 1) on a line passing through (α , 2 α , 5) is ((1/5) , (2/5) , (3/5)) , then α is equal to

Question

If the foot of perpendicular drawn from the point (2,5 , 1) on a line passing through (α , 2 α , 5) is ((1/5) , (2/5) , (3/5)) , then α is equal to (A) (19/9) (B) (11/570) (C) (57/54) (D) (1/25)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-wr5acebtf7oh.png" /> From diagram overset arrow P Q⋅ overset arrow Q R=0 [(2 - (1/5)) hati + (5 - (2/5)) hatj + (1 - (3/5)) hatk]⋅ [(α - (1/5)) hati + (2 α - (2/5)) hatj + (5 - (3/5)) hatk]=0 ⇒ (9 α /5)-(9/25)+(46 α /5)-(46/25)+(44/25)=0 ⇒ α =(1/25)

Q. If the foot of perpendicular drawn from the point $(2, 5, 1)$ on a line passing through $(α, 2 α, 5)$ is $(\frac{1}{5}, \frac{2}{5}, \frac{3}{5})$ , then $α$ is equal to

$\frac{19}{9}$

$\frac{11}{570}$

$\frac{57}{54}$

$\frac{1}{25}$

Q. If the foot of perpendicular drawn from the point (2,5,1) on a line passing through (α,2α,5) is (51​,52​,53​) , then α is equal to

919​

57011​

5457​

251​

From diagram PQ→​⋅QR→​=0 [(2−51​)i^+(5−52​)j^​+(1−53​)k^]⋅[(α−51​)i^+(2α−52​)j^​+(5−53​)k^]=0 ⇒59α​−259​+546α​−2546​+2544​=0 ⇒α=251​

Q. If the foot of perpendicular drawn from the point $(2, 5, 1)$ on a line passing through $(α, 2 α, 5)$ is $(\frac{1}{5}, \frac{2}{5}, \frac{3}{5})$ , then $α$ is equal to

$\frac{19}{9}$

$\frac{11}{570}$

$\frac{57}{54}$

$\frac{1}{25}$