PYQ Vault

Day 17: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Three Dimensional Geometry. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    34 (a)
    Find the image A' of the point A(1, 6, 3) in the line x1=y−12=z−23\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}. Also, find the equation of the line joining A and A'.

  2. Question 2

    Three Dimensional Geometry. Asked 2 times: 2023*, 2025 (* = numbers or wording changed that year)

    35
    Find the foot of the perpendicular drawn from point (2,−1,5)(2, -1, 5) to the line x−1110=y+2−4=z+8−11\dfrac{x - 11}{10} = \dfrac{y + 2}{-4} = \dfrac{z + 8}{-11}. Also, find the length of the perpendicular.

  3. Question 3

    Three Dimensional Geometry. Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)

    35 (b)
    Find the equation of a line in vector and cartesian form which passes through the point (1,2,−4)(1, 2, -4) and is perpendicular to the lines x−83=y+19−16=z−107\frac{x - 8}{3} = \frac{y + 19}{-16} = \frac{z - 10}{7}, and r⃗=15i^+29j^+5k^+μ(3i^+8j^−5k^)\vec{r} = 15\hat{i} + 29\hat{j} + 5\hat{k} + \mu(3\hat{i} + 8\hat{j} - 5\hat{k}).

  4. Question 4

    Vector Algebra. Asked 2 times: 2022, 2025

    24 (b)
    Vector r⃗\vec{r} is inclined at equal angles to the three axes x, y and z. If magnitude of r⃗\vec{r} is 535\sqrt{3} units, then find r⃗\vec{r}.

  5. Question 5

    Vector Algebra. Asked 2 times: 2022, 2025

    30 (b)
    If a⃗\vec{a} and b⃗\vec{b} are unit vectors inclined with each other at an angle θ\theta, then prove that 12∣a⃗−b⃗∣=sin⁡θ2\dfrac{1}{2}|\vec{a} - \vec{b}| = \sin\dfrac{\theta}{2}.