Match the following. List-I List-II (A) Foot of perpendicular drawn from point ( 1 , 2 , 3 ) to the line 2 x − 2 = 3 y − 1 = 4 z − 2 is. (p) ( 29 107 , 29 30 , 29 69 ) (B) Image of the poi

Question

Match the following.

List-I	List-II
(A) Foot of perpendicular drawn from point $(1, 2, 3)$ to the line $\frac{x - 2}{2} = \frac{y - 1}{3} = \frac{z - 2}{4}$ is.	(p) $(\frac{107}{29}, \frac{30}{29}, \frac{69}{29})$
(B) Image of the point $(1, 2, 3)$ in the line $\frac{x - 2}{2} = \frac{y - 1}{3} = \frac{z - 2}{4}$ is.	(q) $(\frac{88}{29}, \frac{125}{29}, \frac{69}{29})$
(C) Foot of perpendicular from the point $(2, 3, 5)$ to the plane $2 x + 3 y - 4 z + 17 = 0$ is.	(r) $(\frac{107}{29}, \frac{125}{29}, \frac{185}{29})$
(D) Image of the point $(2, 5, 1)$ in the plane $3 x - 2 y + 4 z - 5 = 0$ is.	(s) $(\frac{68}{29}, \frac{44}{29}, \frac{78}{29})$
	(t) $(\frac{38}{29}, \frac{57}{29}, \frac{185}{29})$

TestHub · Accepted Answer

(A) Let the foot be ( 2 + 2 λ , 1 + 3 λ , 2 + 4 λ ) ; perpendicularity: 2 ( 2 λ + 1 ) + 3 ( 3 λ − 1 ) + 4 ( 4 λ − 1 ) = 0 ⇒ 29 λ = 5 ⇒ λ = 29 5 ​ . Foot = ( 29 68 ​ , 29 44 ​ , 29 78 ​ ) → s. (B) Image ( a , b , c ) : 2 1 + a ​ = 29 68 ​ , 2 2 + b ​ = 29 44 ​ , 2 3 + c ​ = 29 78 ​ ⇒ ( 29 107 ​ , 29 30 ​ , 29 69 ​ ) → p. (C) 2 x − 2 ​ = 3 y − 3 ​ = − 4 z − 5 ​ = − 29 4 + 9 − 20 + 17 ​ = − 29 10 ​ : foot = ( 29 38 ​ , 29 57 ​ , 29 185 ​ ) → t. (D) 3 x − 2 ​ = − 2 y − 5 ​ = 4 z − 1 ​ = − 2 ⋅ 29 6 − 10 + 4 − 5 ​ = 29 10 ​ : image = ( 29 88 ​ , 29 125 ​ , 29 69 ​ ) → q .

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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