NDA 2024 Maths · Mathematics · Three Dimensional Geometry · medium

Consider the points A(1,2,3), B(2,4,6) and C(3,6,9). 1. A, B, C are collinear. 2. B divides AC in the ratio 2:1.

Single correct option

Consider the points

A(1,2,3)

B(2,4,6)

and

C(3,6,9)

.
1.

A

B

C

are collinear.
2.

B

divides

AC

in the ratio

2:1

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) 1 only

The vectors

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

and

\vec{AC}=(2,4,6)

are proportional, so the points are collinear and statement 1 is true. Also

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

, so

B

is the midpoint of

AC

and divides it in the ratio

1:1

, not

2:1

; statement 2 is false. Trap:

AC=2AB

tempts the ratio

2:1

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