Find the projection of the line segment joini | vedclass

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(D) The direction ratios of the line are $a = 6, b = 2, c = 3$.The direction cosines $(l, m, n)$ are given by:$l = \frac{6}{\sqrt{6^2 + 2^2 + 3^2}} =

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$22/7$

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(D) The direction ratios of the line are $a = 6, b = 2, c = 3$.The direction cosines $(l, m, n)$ are given by:$l = \frac{6}{\sqrt{6^2 + 2^2 + 3^2}} = \frac{6}{\sqrt{36 + 4 + 9}} = \frac{6}{\sqrt{49}} = \frac{6}{7}$$m = \frac{2}{\sqrt{49}} = \frac{2}{7}$$n = \frac{3}{\sqrt{49}} = \frac{3}{7}$The projection of the line segment joining points $P(x_1, y_1, z_1) = (-1, 0, 3)$ and $Q(x_2, y_2, z_2) = (2, 5, 1)$ on the line is given by:$Projection = l(x_2 - x_1) + m(y_2 - y_1) + n(z_2 - z_1)$Substituting the values:$Projection = \frac{6}{7}(2 - (-1)) + \frac{2}{7}(5 - 0) + \frac{3}{7}(1 - 3)$$Projection = \frac{6}{7}(3) + \frac{2}{7}(5) + \frac{3}{7}(-2)$$Projection = \frac{18}{7} + \frac{10}{7} - \frac{6}{7}$$Projection = \frac{18 + 10 - 6}{7} = \frac{22}{7}$

Find the projection of the line segment joining the points $(-1, 0, 3)$ and $(2, 5, 1)$ on a line whose direction ratios are $6, 2, 3$.

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