Values of x and y for which vectors vec A = left( {6hat{i} + xhat{j} - 2hat{k}} right) a

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3-1.Vectors

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The values of $x$ and $y$ for which vectors $\vec A = \left( {6\hat i + x\hat j - 2\hat k} \right)$ and $\vec B = \left( {5\hat i - 6\hat j - y\hat k} \right)$ may be parallel are

A$x = 0$, $y = \frac{2}{3}$

B$x = - \frac{{36}}{5},y = \frac{5}{3}$

C$x = - \frac{{15}}{3},y = \frac{{23}}{5}$

D$x = \frac{{36}}{5},y = \frac{{15}}{4}$

Solution

For vectors to be parallel, ratio of coefficients should be same.
$\therefore \quad \frac{6}{5}=\frac{x}{-6}=\frac{-2}{-y}$

Standard 11

Physics

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(JEE MAIN-2022)