The set of real values of lambda for which th | vedclass

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(D) Two vectors $\vec{a}$ and $\vec{b}$ are perpendicular if their dot product is zero,i.e.,$\vec{a} \cdot \vec{b} = 0$. Given vectors are $\vec{a} =

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$\phi$

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(D) Two vectors $\vec{a}$ and $\vec{b}$ are perpendicular if their dot product is zero,i.e.,$\vec{a} \cdot \vec{b} = 0$. Given vectors are $\vec{a} = \lambda \hat{i} - 3 \hat{j} + 5 \hat{k}$ and $\vec{b} = 2 \lambda \hat{i} - \lambda \hat{j} + \hat{k}$. Calculating the dot product: $(\lambda \hat{i} - 3 \hat{j} + 5 \hat{k}) \cdot (2 \lambda \hat{i} - \lambda \hat{j} + \hat{k}) = 0$ $2 \lambda^2 + 3 \lambda + 5 = 0$ For this quadratic equation,the discriminant $D = b^2 - 4ac = (3)^2 - 4(2)(5) = 9 - 40 = -31$. Since $D Therefore,the set of real values is $\phi$.

The set of real values of $\lambda$ for which the vectors $\lambda \hat{i}-3 \hat{j}+5 \hat{k}$ and $2 \lambda \hat{i}-\lambda \hat{j}+\hat{k}$ are perpendicular to each other is

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