The direction ratios of the line bisecting th | vedclass

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(A) The direction ratios of the $x$-axis are $(1, 0, 0)$. The unit vector along the $x$-axis is $\hat{a} = (1, 0, 0)$.Let the given line have directio

Vedclass · Accepted Answer

$(\frac{3}{\sqrt{35}}+1, -\frac{1}{\sqrt{35}}, \frac{5}{\sqrt{35}})$

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(A) The direction ratios of the $x$-axis are $(1, 0, 0)$. The unit vector along the $x$-axis is $\hat{a} = (1, 0, 0)$.Let the given line have direction ratios $(3, -1, 5)$. The magnitude is $\sqrt{3^2 + (-1)^2 + 5^2} = \sqrt{9 + 1 + 25} = \sqrt{35}$.The unit vector along this line is $\hat{b} = (\frac{3}{\sqrt{35}}, -\frac{1}{\sqrt{35}}, \frac{5}{\sqrt{35}})$.The angle bisector of two unit vectors $\hat{a}$ and $\hat{b}$ is given by the vector $\hat{a} + \hat{b}$.$\hat{a} + \hat{b} = (1 + \frac{3}{\sqrt{35}}, 0 - \frac{1}{\sqrt{35}}, 0 + \frac{5}{\sqrt{35}}) = (\frac{\sqrt{35}+3}{\sqrt{35}}, -\frac{1}{\sqrt{35}}, \frac{5}{\sqrt{35}})$.Multiplying by $\sqrt{35}$, the direction ratios are $(\sqrt{35}+3, -1, 5)$.

The direction ratios of the line bisecting the angle between the $x$-axis and the line having direction ratios $(3, -1, 5)$ are

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