Let ABC be a triangle with vertices at points A (2, 3, 5), B (-1, 3, 2) and C (λ, 5, μ) in three dimensional space. If the median through A is equally inclined with the axes, then (λ, μ) is equal to:

Question

Let ABC be a triangle with vertices at points A (2, 3, 5), B (-1, 3, 2) and C (λ, 5, μ) in three dimensional space. If the median through A is equally inclined with the axes, then (λ, μ) is equal to: (A) (10,7) (B) (7,5) (C) (7,10) (D) (5,7)

Tardigrade Admin · Accepted Answer

Since AD is the median ∴ D=((λ-1/2) ,4, (μ+2/2)) Now, dRâs of AD is a=((λ-1/2)-2)=(λ-5/2) b=4-3=1, c=(μ+2/2)-5=(μ-8/2) Also, a, b, c are dRâs ∴ a=kl, b =km, c=kn where I = m = n and l2+m2+n2=1 ⇒ l = m = n =(1/√3) Now, a = 1,b = 1 and c = 1 ⇒ λ=7 and μ=10

Q. Let $A BC$ be a triangle with vertices at points $A (2, 3, 5), B (- 1, 3, 2)$ and $C (λ, 5, μ)$ in three dimensional space. If the median through A is equally inclined with the axes, then $(λ, μ)$ is equal to:

$(10, 7)$

$(7, 5)$

$(7, 10)$

$(5, 7)$

Q. Let ABC be a triangle with vertices at points A(2,3,5),B(−1,3,2) and C(λ,5,μ) in three dimensional space. If the median through A is equally inclined with the axes, then (λ,μ) is equal to:

(10,7)

(7,5)

(7,10)

(5,7)

Since AD is the median ∴D=(2λ−1​,4,2μ+2​) Now, dR’s of AD is a=(2λ−1​−2)=2λ−5​ b=4−3=1,c=2μ+2​−5=2μ−8​ Also, a, b, c are dR’s ∴a=kl,b=km,c=kn where I=m=n and l2+m2+n2=1 ⇒l=m=n=3​1​ Now, a=1,b=1 and c=1 ⇒λ=7andμ=10

Q. Let $A BC$ be a triangle with vertices at points $A (2, 3, 5), B (- 1, 3, 2)$ and $C (λ, 5, μ)$ in three dimensional space. If the median through A is equally inclined with the axes, then $(λ, μ)$ is equal to:

$(10, 7)$

$(7, 5)$

$(7, 10)$

$(5, 7)$