The mirror image of the point (1,2, 3) in a plane is (-(7/3), -(4/3), -(1/3)). Which of the following points lies on this plane ?

Question

The mirror image of the point (1,2, 3) in a plane is (-(7/3), -(4/3), -(1/3)). Which of the following points lies on this plane ? (A) (1, -1 ,1 ) (B) ( - 1 , - 1 , 1 ) (C) (1 ,1 ,1 ) (D) ( - 1 , - 1 , - 1 )

Tardigrade Admin · Accepted Answer

Point on plane R(-(7/3), -(4/3), -(1/3)) Normal vector of plane is (10/3) hati + (10/3) hatj + (10/3) hatk Equation of require plane is x + y + z = 1 Hence (1, -1, 1) lies on plane

Q. The mirror image of the point $(1, 2, 3)$ in a plane is $(- \frac{7}{3}, - \frac{4}{3}, - \frac{1}{3}) .$ Which of the following points lies on this plane ?

$(1, - 1, 1)$

$(- 1, - 1, 1)$

$(1, 1, 1)$

$(- 1, - 1, - 1)$

Point on plane $R (- \frac{7}{3}, - \frac{4}{3}, - \frac{1}{3})$
Normal vector of plane is $\frac{10}{3} \hat{i} + \frac{10}{3} \hat{j} + \frac{10}{3} \hat{k}$
Equation of require plane is $x + y + z = 1$
Hence $(1, - 1, 1)$ lies on plane

Q. The mirror image of the point (1,2,3) in a plane is (−37​,−34​,−31​). Which of the following points lies on this plane ?

(1,−1,1)

(−1,−1,1)

(1,1,1)

(−1,−1,−1)