If the distance between the points (7,1,−3) and (4,5,λ) is 13 units, then what is one of the values of λ ?

Engineering

Mathematics

Distance Formulae and Its Application

Distance from a Plane

Question

If the distance between the points (7,1,−3) and (4,5,λ) is 13 units, then what is one of the values of λ ?

A

8

B

9

C

10

D

20

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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+[λ²+ 6λ + 9]λ² + 6λ + 9

= 144 ⇒ λ² + 6λ − 135 = 0

∴ λ = 9 − 15

∴ λ = 9