PYQ Vault

Day 288: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2022

    4
    If a⃗=i^+j^+k^\vec{a} = \hat{i} + \hat{j} + \hat{k}, a⃗⋅b⃗=1\vec{a} \cdot \vec{b} = 1 and a⃗×b⃗=j^−k^\vec{a} \times \vec{b} = \hat{j} - \hat{k}, then find ∣b⃗∣\left|\vec{b}\right|.

  2. Question 2

    Vector Algebra. Asked once: 2022

    9 (a)
    Let a⃗=i^+j^\vec{a} = \hat{i} + \hat{j}, b⃗=i^−j^\vec{b} = \hat{i} - \hat{j} and c⃗=i^+j^+k^\vec{c} = \hat{i} + \hat{j} + \hat{k}. If n^\hat{n} is a unit vector such that a⃗⋅n^=0\vec{a} \cdot \hat{n} = 0 and b⃗⋅n^=0\vec{b} \cdot \hat{n} = 0, then find ∣c⃗⋅n^∣\left|\vec{c} \cdot \hat{n}\right|.

  3. Question 3

    Vector Algebra. Asked once: 2022

    10
    If a⃗\vec{a} and b⃗\vec{b} are two vectors such that a⃗=i^−j^+k^\vec{a} = \hat{i} - \hat{j} + \hat{k} and b⃗=2i^−j^−3k^\vec{b} = 2\hat{i} - \hat{j} - 3\hat{k}, then find the vector c⃗\vec{c}, given that a⃗×c⃗=b⃗\vec{a} \times \vec{c} = \vec{b} and a⃗⋅c⃗=4\vec{a} \cdot \vec{c} = 4.

  4. Question 4

    Vector Algebra. Asked once: 2022

    7 (a)
    If a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} and d⃗\vec{d} are four non-zero vectors such that a⃗×b⃗=c⃗×d⃗\vec{a} \times \vec{b} = \vec{c} \times \vec{d} and a⃗×c⃗=4b⃗×d⃗\vec{a} \times \vec{c} = 4\vec{b} \times \vec{d}, then show that (a⃗−2d⃗)(\vec{a} - 2\vec{d}) is parallel to (2b⃗−c⃗)(2\vec{b} - \vec{c}) where a⃗≠2d⃗\vec{a} \neq 2\vec{d}, c⃗≠2b⃗\vec{c} \neq 2\vec{b}.