PYQ Vault
EbooksTutor

|a| = 1, |b| = 4, a . b = 2 and c = 2(a x b) - 3b: find b . c or the angle between b and c

The same question, asked 3 times: 30 Jan 2023*, 30 Jan 2024*, 31 Jan 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    30 Jan 2023

    159
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two vectors, Let ∣a→∣=1,∣b→∣=4|\overrightarrow{a}| = 1,|\overrightarrow{b}| = 4 and a→⋅b→=2\overrightarrow{a}\cdot\overrightarrow{b}= 2. If c→=(2a→×b→)−3b→\overrightarrow{c}= (2\overrightarrow{a}\times\overrightarrow{b}) - 3\overrightarrow{b}, then the value of b→⋅c→\overrightarrow{b}\cdot\overrightarrow{c} is

    Tap an option to check your answer.

  2. Question 2

    30 Jan 2024

    64
    Let a→=a1i^+a2j^+a3k^\overrightarrow{a}=a_{1}\widehat{i}+a_{2}\widehat{j}+a_{3}\widehat{k} and b→=b1i^+b2j^+b3k^\overrightarrow{b}=b_{1}\widehat{i}+b_{2}\widehat{j}+b_{3}\widehat{k} be two vectors such that ∣a→∣=1;a→⋅b→=2|\overrightarrow{a}| = 1;\overrightarrow{a}\cdot\overrightarrow{b}= 2 and ∣b→∣=4|\overrightarrow{b}| = 4. If c→=2(a→×b→)−3b→\overrightarrow{c}= 2(\overrightarrow{a}\times\overrightarrow{b}) - 3\overrightarrow{b}, then the angle between b→\overrightarrow{b} and c→\overrightarrow{c} is equal to:

    Tap an option to check your answer.

  3. Question 3

    31 Jan 2024

    88
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two vectors such that ∣a→∣=1,∣b→∣=4|\overrightarrow{a}| = 1,|\overrightarrow{b}| = 4 and a→⋅b→=2\overrightarrow{a}\cdot\overrightarrow{b}= 2. If c→=(2a→×b→)−3b→\overrightarrow{c}= (2\overrightarrow{a}\times\overrightarrow{b}) - 3\overrightarrow{b} and the angle between b→\overrightarrow{b} and c→\overrightarrow{c} is α\alpha, then 192sin⁡2α192\sin^{2}\alpha is equal to