Question

ΔABC has vertices at A = (2, 3, 5), B = (–1, 3, 2) and C = (λ, 5, µ). If the median through A is equally inclined to the axes, then the values of λ and µ respectively are ______.

पर्याय

• 10, 7

• 9, 10

• 7, 9

• 7, 10

Answer 1

ΔABC has vertices at A = (2, 3, 5), B = (–1, 3, 2) and C = (λ, 5, µ). If the median through A is equally inclined to the axes, then the values of λ and µ respectively are 7, 10.

Explanation:

It is given that, A = (2, 3, 5), B = (–1, 3, 2) and C = (λ, 5, µ) are three vertices of ΔABC.

Let D be the mid-point of BC

So, coordinates of D = `((λ - 1)/2, (5 + 3)/2, (µ + 2)/2)`

= `((λ - 1)/2, 4, (µ + 2)/2)`

So, direction ratios of

AD = `((λ - 1)/2 - 2, 4 - 3, (µ + 2)/2 - 5)`

= `((λ - 5)/2, 1, (µ - 8)/2)`

As, AD is equally inclined to both the coordinates axes.

Therefore, `(λ - 5)/2 = 1 =(µ - 8)/2`

`\implies (λ - 5)/2` = 1

`\implies` λ = 7

And, 1 = `(µ - 8)/2`

`\implies` µ = 10