During a cricket match, the position of the bowler, the wicket keeper and the leg slip fielder are in a line given by B=2i+8j, W=6i+12j and F=12i+18j respectively. Calculate the ratio in which the wicketkeeper divides the line segment joining the bowler and the leg slip fielder.

MathsCBSE Class 12 · Board exam 2025, set 65/1/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2025: question 29(b)

Set in the CBSE Class 12 board exam of 2025, paper 65/1/1, section C, question 29(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(b) · 3 marks · Short answerCompetency-basedVector Algebra

During a cricket match, the position of the bowler, the wicket keeper and the leg slip fielder are in a line given by $B = 2 \hat{i} + 8 \hat{j}$ , $W = 6 \hat{i} + 12 \hat{j}$ and $F = 12 \hat{i} + 18 \hat{j}$ respectively. Calculate the ratio in which the wicketkeeper divides the line segment joining the bowler and the leg slip fielder.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 65/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Assume W divides BF in the ratio $k : 1$ .

Hint 2

Use the section formula $\frac{k F + B}{k + 1}$ and equate it to $W$ component by component.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Let W divide BF in the ratio $k : 1$ . By the section formula, $W = \frac{k F + 1 \cdot B}{k + 1}$ .
1 mark
So $6 \hat{i} + 12 \hat{j} = (\frac{12 k + 2}{k + 1}) \hat{i} + (\frac{18 k + 8}{k + 1}) \hat{j}$ .
1 mark
Compare the $\hat{i}$ components: $12 k + 2 = 6 k + 6 \Rightarrow k = \frac{2}{3}$ . The $\hat{j}$ components give $18 k + 8 = 12 k + 12$ , which also gives $k = \frac{2}{3}$ , so the points are collinear. Hence the wicket keeper divides BF in the ratio $2 : 3$ (internally).
1 mark

Answer: $2 : 3$

Where the marks are

Applies the section formula with ratio $k : 1$ (1 mark)
Writes the components in terms of $k$ (1 mark)
Solves $k = \frac{2}{3}$ and states the ratio $2 : 3$ (1 mark)

Revise the chapter

Chapter: Vector Algebra (notes, formulas, where marks are lost and every past question)
Topic: Section Formula and Collinearity of Vectors

Practise this chapterBoard-style questions from Vector Algebra, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 29(b)

Hints

Step-by-step solution

Revise the chapter

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