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Choose the correct option.
If the vectors aî + 3ĵ - 2k̂ and 3î - 4ĵ + bk̂ are collinear, then (a, b) =
If the vectors $a\hat{i} + 3\hat{j} - 2\hat{k}$ and $3\hat{i} - 4\hat{j} + b\hat{k}$ are collinear, then $(a, b) =$
- (a)$\left(\frac{9}{4}, \frac{8}{3}\right)$
- (b)$\left(-\frac{9}{4}, \frac{8}{3}\right)$
- (c)$\left(\frac{9}{4}, -\frac{8}{3}\right)$
- (d)$\left(-\frac{9}{4}, -\frac{8}{3}\right)$
Answer
Answer
Correct option: (b)
Answer: (b) $\left(-\frac{9}{4}, \frac{8}{3}\right)$
Collinear vectors have proportional components: $\frac{a}{3} = \frac{3}{-4} = \frac{-2}{b}$.
So $a = -\frac{9}{4}$ and $b = \frac{8}{3}$.