MathsCBSE Class 12 · Board exam 2023, set 65/5/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2023: question 30(b)

Set in the CBSE Class 12 board exam of 2023, paper 65/5/1, section C, question 30(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(b) · 3 marks · Short answerVector Algebra

Three vectors $a$ , $b$ and $c$ satisfy the condition $a + b + c = 0$ . Evaluate the quantity $μ = a \cdot b + b \cdot c + c \cdot a$ , if $∣ a ∣ = 3$ , $∣ b ∣ = 4$ and $∣ c ∣ = 2$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/5/1.

Hints

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

Hint 1

Square (dot with itself) the given condition $a + b + c = 0$ .

Hint 2

The expansion contains exactly $2 μ$ plus the squares of the magnitudes.

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.

Since $a + b + c = 0$ , we have $(a + b + c) \cdot (a + b + c) = 0$ .
1 mark
$∣ a ∣^{2} + ∣ b ∣^{2} + ∣ c ∣^{2} + 2 (a \cdot b + b \cdot c + c \cdot a) = 0$
$9 + 16 + 4 + 2 μ = 0$
1 mark
$2 μ = - 29$ , so $μ = - \frac{29}{2}$
1 mark

Answer: $μ = - \frac{29}{2}$

Where the marks are

Takes the dot product of $a + b + c$ with itself and equates to 0 (1 mark)
Expands as $∣ a ∣^{2} + ∣ b ∣^{2} + ∣ c ∣^{2} + 2 μ = 0$ (1 mark)
$μ = - \frac{29}{2}$ (1 mark)

Revise the chapter

Chapter: Vector Algebra (notes, formulas, where marks are lost and every past question)
Topic: Scalar (Dot) Product 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 65/5/1: 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 30(b)

Hints

Step-by-step solution

Revise the chapter

More questions from Vector Algebra