If a=2 hat{i}+3 hat{j}-5 hat{k},b=m hat{i}+n | vedclass

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(A) Given vectors are $a=2 \hat{i}+3 \hat{j}-5 \hat{k}$ and $b=m \hat{i}+n \hat{j}+12 \hat{k}$.Since $a 	imes b = 0$,the vectors $a$ and $b$ are coll

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$\left(\frac{-24}{5}, \frac{-36}{5}\right)$

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(A) Given vectors are $a=2 \hat{i}+3 \hat{j}-5 \hat{k}$ and $b=m \hat{i}+n \hat{j}+12 \hat{k}$.Since $a 	imes b = 0$,the vectors $a$ and $b$ are collinear (parallel).For two parallel vectors $a = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$ and $b = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k}$,the components are proportional:$\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}$Substituting the given values:$\frac{2}{m} = \frac{3}{n} = \frac{-5}{12}$From $\frac{2}{m} = \frac{-5}{12}$,we get $m = \frac{2 	imes 12}{-5} = -\frac{24}{5}$.From $\frac{3}{n} = \frac{-5}{12}$,we get $n = \frac{3 	imes 12}{-5} = -\frac{36}{5}$.Therefore,$(m, n) = \left(-\frac{24}{5}, -\frac{36}{5}ight)$.

If $a=2 \hat{i}+3 \hat{j}-5 \hat{k}$,$b=m \hat{i}+n \hat{j}+12 \hat{k}$ and $a \times b=0$,then $(m, n)$ is equal to

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