If the vector a¯=2i^+3j^+6k^ and b¯ are collinear and |b|=21, then b =

a¯,b¯ are collinear⇒b¯=ma¯⇒|b¯|=|m||a¯|⇒|b¯|=|m|4+9+3621=±7mm=±3∴b¯=±3a¯

If the vector a¯=2i^+3j^+6k^ and b¯ are collinear and |b|=21, then b =

a¯,b¯ are collinear⇒b¯=ma¯⇒|b¯|=|m||a¯|⇒|b¯|=|m|4+9+3621=±7mm=±3∴b¯=±3a¯

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If the vector $\bar{a} = 2 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $\bar{b}$ are collinear and $| b | = 21$ , then b =

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$\pm 21 (2 \bar{i} + 3 \bar{j} + 6 \bar{k})$

$\bar{i} + \bar{j} + \bar{k}$

$\pm 3 (2 \bar{i} + 3 \bar{j} + 6 \bar{k})$

$\pm (2 \bar{i} + 3 \bar{j} + 6 \bar{k})$

answer is B.

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Detailed Solution

$\bar{a}, \bar{b} a r e c o l l i n e a r \Rightarrow \bar{b} = m \bar{a}$
$\begin{array}{l} \Rightarrow | \bar{b} | = | m | | \bar{a} | \\ \Rightarrow | \bar{b} | = | m | \sqrt{4 + 9 + 36} \\ 21 = \pm 7 m \\ m = \pm 3 \\ ∴ \bar{b} = \pm 3 \bar{a} \end{array}$