Vector Algebra 5 marks Questions, CBSE Class 12 PYQs 2024–2026

1 different 5 marks questions on Vector Algebra from CBSE Class 12 Maths board exams 2024–2026, newest first.

Q355 marksLong AnswerVector Algebra CBSE 2025 · 65/4/1

Show that the area of a parallelogram whose diagonals are represented by $a$ and $b$ is given by $\frac{1}{2} ∣ a \times b ∣$ . Also find the area of a parallelogram whose diagonals are $2 i^- j^+ k^$ and $i^+ 3 j^- k^$ .

Show answer & solution

Answer: Proved; area

= \frac{62}{2}

sq. units

Let the adjacent sides be $p, q$ ; then $a = p + q$ , $b = q - p$ (or $p - q$ ).
$a \times b = (p + q) \times (q - p) = p \times q - q \times p = 2 (p \times q)$ .
Area $= ∣ p \times q ∣ = \frac{1}{2} ∣ a \times b ∣$ .
$(2 i^- j^+ k^) \times (i^+ 3 j^- k^) = (1 - 3) i^- (- 2 - 1) j^+ (6 + 1) k^= - 2 i^+ 3 j^+ 7 k^$ .
Magnitude $= 4 + 9 + 49 = 62$ , so area $= \frac{62}{2}$ sq. units.

Also asked in: 2025 65/4/2, 2025 65/4/3

Vector Algebra: 5 marks Questions (CBSE Class 12)