Question
If $|\vec{a}-\vec{b}|=|\vec{a}+\vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ will be -

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If $\text{g}'(\text{x})=\int\text{x}^\text{x}\log_\text{e}(\text{ex})\text{dx}$ then $\text{g}(\pi)$ equals:
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If $y=\cos ^{-1}\left(e^x\right)$, then $\frac{d y}{d x}$ is :
The number of solutions for the equation $ 2\sin ^{ -1 }{ \sqrt { { \text{x} }^{ 2 }- \text{x}+1 } } +\cos ^{ -1 }{ \sqrt { { \text{x} }^{ 2 }- \text{x} } } =\frac { 3\pi }{ 2 }$ is:
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The shortest distance between the lines $\frac{\text{x}-3}{3}=\frac{\text{y}-8}{-1}=\frac{\text{z}-3}{1}$ and, $\frac{\text{x}+3}{-3}=\frac{\text{y}+7}{2}=\frac{\text{z}-6}{4}$ is:
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If $\text{f(x)}=\log_{\text{x}^2}(\log\text{x}),$ the f(x) at x = e is:
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$Z = 20x_1 + 20x_2,$ subject to $\text{x}1\geq0,\text{x}_{2}\geq0,\text{x}_{1}+2\text{x}_{2}\geq8,3\text{x}_{1}+2\text{x}_{2}\geq15,5\text{x}_{1}+2\text{x}_{2}\geq20.$ The minimum value of $Z$ occurs at