NIMCET 2020 — Mathematics PYQ

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Question

NIMCET 2020 — Mathematics PYQ

NIMCET | Mathematics | 2020

If $a$ , $b$ , $c$ are three non-zero vectors with no two of which are collinear, $a + 2 b$ is collinear with $c$ and $b + 3 c$ is collinear with $a$ , then $∣ a + 2 b + 6 c ∣$ will be equal to

Choose the correct answer:

Explanation

Cocept:
If a vector A is collinear to other vector B, it can be written as:
$A = λ \times B$ where $λ$ is any scalar number

Calculation:

Given $a + 2 b$ is collinear with $c$
$\Rightarrow a + 2 b = λ_{1} \times c$
$\dots (i)$

Also given $b + 3 c$ is collinear with $a$
$\Rightarrow b + 3 c = λ_{2} \times a$
$\dots (ii)$

Subtracting $2 \times (ii)$ from (i)
$\Rightarrow a - 6 c = λ_{1} c - 2 λ_{2} a$
$∴ λ_{1} = - 6$ , $λ_{2} = \frac{1}{2}$

From (ii)
$\Rightarrow b + 3 c = - \frac{1}{2} a$
$\Rightarrow 2 b + 6 c = - a$
$\Rightarrow a + 2 b + 6 c = 0$
$\Rightarrow ∣ a + 2 b + 6 c ∣ = 0$

Choose the correct answer:

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