MHT CET · Maths · Vector Algebra

$L$ and $M$ are two points with position vectors $2 \vec{a} - \vec{b}$ and $\vec{a} + 2 \vec{b}$ respectively. The position vector of the point $N$ which divides the line segment $L M$ in the ratio $2 : 1$ externally is

A $3 \vec{b}$
B $4 \vec{b}$
C $5 \vec{b}$
D $3 \vec{a} + 4 \vec{b}$

Verified Solution

Answer & Solution

Correct Answer

(C) $5 \vec{b}$

Step-by-step Solution

Detailed explanation

Since point

N (\bar{n})

divides LM in ratio 2:1 externally

\Rightarrow \bar{n} = \frac{2 (\bar{m}) - \bar{l}}{2 - l}

(Using section formula)

\Rightarrow \bar{n} = 2 (\bar{a} + 2 \bar{b}) - (2 \bar{a} - \bar{b})

\Rightarrow \bar{n} = 2 \bar{a} + 4 \bar{b} - 2 \bar{a} + \bar{b}

\Rightarrow \bar{n} = 5 \bar{b}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app

L and M are two points with position vectors 2 a → − b → and a → +2 b → respectively. The position vector of the point N which divides the line segment LM in the ratio 2:1 externally is

Step-by-step Solution

$L$ and $M$ are two points with position vectors $2 \vec{a} - \vec{b}$ and $\vec{a} + 2 \vec{b}$ respectively. The position vector of the point $N$ which divides the line segment $L M$ in the ratio $2 : 1$ externally is