Let P Q R be a triangle with R ( - 1 , 4 , 2 ) . Suppose M ( 2 , 1 , 2 ) is the mid point of P Q . The distance of the centroid of ∆ P Q R from the point of intersection of the line x - 2 0 = y 2 = z + 3 - 1 and x - 1 1 = y + 3 - 3 = z + 1

Question

Let P Q R be a triangle with R ( - 1 , 4 , 2 ) . Suppose M ( 2 , 1 , 2 ) is the mid point of P Q . The distance of the centroid of ∆ P Q R from the point of intersection of the line x - 2 0 = y 2 = z + 3 - 1 and x - 1 1 = y + 3 - 3 = z + 1 1 is

Quantrex Academy · Accepted Answer

Correct answer: C. 69

Given: x - 2 0 = y 2 = z + 3 - 1 and x - 1 1 = y + 3 - 3 = z + 1 1 ⇒ x - 2 0 = y 2 = z + 3 - 1 = k let ⇒ x = 2 , y = 2 k , z = - k + 3 . . . i Also, x - 1 1 = y + 3 - 3 = z + 1 1 = λ let ⇒ x = λ + 1 , y = - 3 λ - 3 . z = λ - 1 . . . i i Using i and i i , ⇒ 2 = λ + 1 , 2 k = - 3 λ - 3 ⇒ λ = 1 , 2 k = - 3 - 3 ⇒ λ = 1 , k = - 3 ⇒ x = 2 , y = - 6 , z = 0 So, the intersection point of two given lines is 2 , - 6 , 0 . Now, we know that centroid G divides M R (median) in the ratio 1 : 2 . So, by using section formula, G ≡

Let P Q R be a triangle with R ( - 1 , 4 , 2 ) . Suppose M ( 2 , 1 , 2 ) is the mid point of P Q . The distance of the centroid of ∆ P Q R from the point of intersection of the line x - 2 0 = y 2 = z + 3 - 1 and x - 1 1 = y + 3 - 3 = z + 1 1 is

Options

Correct answer

Step-by-step solution

More from Three Dimensional Geometry