If the distance between the points \left(\right. 7 , 1 , - 3 \left.\right) and \left(\right. 4 , 5 , \lambda \left.\right) is 13 units, then what is one of the values of \lambda?

Engineering

Mathematics

Line of Greatest Slope

Question

If the distance between the points

(7, 1, - 3)

and

(4, 5, λ)

13

units, then what is one of the values of

λ

20

10

9

8

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Given two points A(7,1,-3) and B(4,5,

λ

)

total distance=13units ,

λ

distance of AB

= \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}} 13 = \sqrt{(4 - 7)^{2} + (5 - 1)^{2} + (λ + 3)^{2}} 169 = 9 + 16 + [λ^{2} + 6 λ + 9] {λ,}^{2} + 6 λ + 9 = 144 \Rightarrow {λ,}^{2} + 6 λ - 135 = 0 ∴ λ = 9, - 15 ∴ λ = 9

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