MathsCBSE Class 12 · Board exam 2023, set 65/1/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2023: question 23(a)

Set in the CBSE Class 12 board exam of 2023, paper 65/1/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(a) · 2 marks · Very short answerVector Algebra

Position vectors of the points A, B and C as shown in the figure below are $a$ , $b$ and $c$ respectively. If $A C = \frac{5}{4} A B$ , express $c$ in terms of $a$ and $b$ .

Figure in the paper: A horizontal line with three points in order from left to right: A( $a$ ), B( $b$ ), C( $c$ ), with C beyond B. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/1/1.

Hints

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

Hint 1

Write any vector $P Q$ as (position vector of Q) − (position vector of P).

Hint 2

Substitute this into $A C = \frac{5}{4} A B$ and make $c$ the subject.

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.

$A C = c - a$ and $A B = b - a$ . So $c - a = \frac{5}{4} (b - a)$ .
1½ marks
$c = a + \frac{5}{4} b - \frac{5}{4} a = \frac{5 b}{4} - \frac{a}{4}$ , i.e. $c = \frac{5 b - a}{4}$ .
½ mark

Answer: $c = \frac{5 b - a}{4}$

Where the marks are

Writes $c - a = \frac{5}{4} (b - a)$ (1½ marks)
Simplifies to $c = \frac{5 b}{4} - \frac{a}{4}$ (½ 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 paper2023 board paper, set 65/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Mathematics 2023: question 23(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Vector Algebra