QPaperGen

Vector Algebra

Class: 12 | Subject: Math | Topic: Previous year Chapter wise Questions and Answers

MCQ

  1. Let \(A = \{3, 5\}\). Then number of reflexive relations on \(A\) is
    (a) 2 (b) 4 (c) 0 (d) 8
    (2023) Ans

    VSA (2 marks)

    1. If \(\vec{\alpha}\) and \(\vec{\beta}\) are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such that \(QR=\frac{3}{2}QP\).
      (AI 2016) An
    2. If \(\vec{\alpha}\) and \(\vec{\beta}\) are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such that \(QR=\frac{3}{2}QP\).
      (AI 2016) An
Find a vector $\vec{a}$ of magnitude $5\sqrt{2}$, making an angle of $\frac{\pi}{4}$ with x-axis, $\frac{\pi}{2}$ with y-axis and an acute angle $\theta$ with z-axis.
(AI-2014) Ans
  • Find the position vector of a point which divides the join of points with position vectors $\vec{a}-2\vec{b}$ and $2\vec{a}+\vec{b}$ externally in the ratio $2:1$.
    (Delhi 2016) An
  • Write the position vector of the point which divides the join of points with position vectors $3\vec{a}-2\vec{b}$ and $2\vec{a}+3\vec{b}$ in the ratio $2:1$.
    (AI 2016) An
  • Find the unit vector in the direction of the sum of the vectors $2\hat{i}+3\hat{j}-\hat{k}$ and $4\hat{i}-3\hat{j}+2\hat{k}$.
    (Foreign 2015)
  • Find a vector in the direction of $\vec{a}=\hat{i}-2\hat{j}$ that has magnitude 7 units.
    (Delhi 2015C)
  • Write the direction ratios of the vector $3\vec{a}+2\vec{b}$ where $\vec{a}=\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$.
    (AI 2015C) An
  • Write a unit vector in the direction of the sum of the vectors $\vec{a}=2\hat{i}+2\hat{j}-5\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-7\hat{k}$.
    (Delhi 2014)
  • SA (3 marks)

    1. Using integration, find the area of the region \(\{(x, y): 4x^2 + 9y^2 \le 36, 2x + 3y \ge 6\}\).
      (2024) Ans

      LA (5 marks)

      1. Using integration, find the area of the region \(\{(x, y): 4x^2 + 9y^2 \le 36, 2x + 3y \ge 6\}\).
        (2024) Ans