Let 2a→=b→×c→+2b→ where a→, b→ and c→ are three unit vectors, then sum of all possible values of 3a→+4b→+5c→ is

Correct answer: (C) 14. 2a→=b→×c→+2b→ Taking dot with b→ 2a→⋅b→=2b→^2⇒a→⋅b→=1 ⇒a→=b→ also b→×c→=0 (from given equation) ⇒b→=c→ or b→=-c→ So, if b→=c→, then 3a→+3b→+5c→=12 or if b→=-c→, then 3a→+4b→+5c→=2

Q18 / 100 · NTA Abhyas (JEE Main) 2020 · Mathematics · Vector Algebra

Let $2 \vec{a} = \vec{b} \times \vec{c} + 2 \vec{b}$ where $\vec{a}, \vec{b}$ and $\vec{c}$ are three unit vectors, then sum of all possible values of $|3 \vec{a} + 4 \vec{b} + 5 \vec{c}|$ is

A
$10$
B
$12$
Correct answer
C
$14$
D
$16$

Solution

2 \vec{a} = \vec{b} \times \vec{c} + 2 \vec{b}

Taking dot with

\vec{b}

2 (\vec{a} \cdot \vec{b}) = 2 {|\vec{b}|}^{2} \Rightarrow \vec{a} \cdot \vec{b} = 1

\Rightarrow \vec{a} = \vec{b}

also

\vec{b} \times \vec{c} = 0

(from given equation)

\Rightarrow \vec{b} = \vec{c}

\vec{b} = - \vec{c}

So, if

\vec{b} = \vec{c}

, then

|3 \vec{a} + 3 \vec{b} + 5 \vec{c}| = 12

or if

\vec{b} = - \vec{c}

, then

|3 \vec{a} + 4 \vec{b} + 5 \vec{c}| = 2

Hence, the correct answer is option: 'C'.

Let 2a→=b→×c→+2b→ where a→, b→ and c→ are three unit vectors, then sum of all possible values of 3a→+4b→+5c→ is

Solution

More Vector Algebra Questions

Let $2 \vec{a} = \vec{b} \times \vec{c} + 2 \vec{b}$ where $\vec{a}, \vec{b}$ and $\vec{c}$ are three unit vectors, then sum of all possible values of $|3 \vec{a} + 4 \vec{b} + 5 \vec{c}|$ is