Find the projection of the line segment joini | vedclass

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(C) Let the points be $A(-1, 2, 3)$ and $B(-1, 4, 0)$.The direction ratios of the line segment $AB$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1) = (-1 - (-1

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$1/2$

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(C) Let the points be $A(-1, 2, 3)$ and $B(-1, 4, 0)$.The direction ratios of the line segment $AB$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1) = (-1 - (-1), 4 - 2, 0 - 3) = (0, 2, -3)$.The line makes angles $\alpha = 45^{\circ}, \beta = 60^{\circ}, \gamma = 60^{\circ}$ with the coordinate axes.The direction cosines of the line are $l = \cos(45^{\circ}) = \frac{1}{\sqrt{2}}$,$m = \cos(60^{\circ}) = \frac{1}{2}$,and $n = \cos(60^{\circ}) = \frac{1}{2}$.The projection of a line segment with direction ratios $(a, b, c)$ on a line with direction cosines $(l, m, n)$ is given by $|al + bm + cn|$.Substituting the values: Projection $= |(0)(\frac{1}{\sqrt{2}}) + (2)(\frac{1}{2}) + (-3)(\frac{1}{2})| = |0 + 1 - \frac{3}{2}| = |-\frac{1}{2}| = \frac{1}{2}$.

Find the projection of the line segment joining the points $A(-1, 2, 3)$ and $B(-1, 4, 0)$ on a line which makes angles of $45^{\circ}, 60^{\circ},$ and $60^{\circ}$ with the coordinate axes.

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