NDA 2024 Maths · Mathematics · Three Dimensional Geometry · medium

The points A(1,2,3), B(3,5,4) and C(5,8,λ) are collinear if λ equals

Single correct option

The points

A(1,2,3)

B(3,5,4)

and

C(5,8,\lambda)

are collinear if

\lambda

equals

Show answer and solution

Answer: (A) $5$

\vec{AB}=(2,3,1)

and

\vec{AC}=(4,6,\lambda-3)

. For collinearity

\vec{AC}=2\vec{AB}

, so

\lambda-3=2

and

\lambda=5

. Trap:

\lambda=6

equals

2\times3

and forgets to subtract the

z

-coordinate of

A

, and

\lambda=4

copies the

z

-coordinate of

B

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