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Q.

What is the condition for the vectors $2 i + 3 j - 4 k$ and $3 i - aj + bk$ to be parallel?

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a

$a = - 6, b = - \frac{9}{2}$

b

$a = 4, b = 5$

c

$a = 8, b = 2$

d

$a = - \frac{9}{2}, b = - 6$

answer is A.

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Detailed Solution

For vectors to be parallel

$\frac{Ax}{Bx} = \frac{Ay}{By} = \frac{Az}{Bz}$

$\frac{2}{3} = \frac{3}{- a} = \frac{- 4}{b} \frac{2}{3} = \frac{- 4}{b}$

$\Rightarrow b = - 6 a = \frac{- 9}{2}$

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What is the condition for the vectors 2i+3j–4k and 3i–aj+bkto be parallel?