(D) Let the coordinates of $B$ be $(x, y, z)$.Given the direction cosines $(l, m, n) = (-2/\sqrt{17}, 3/\sqrt{17}, -2/\sqrt{17})$ and the length $r =

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(D) Let the coordinates of $B$ be $(x, y, z)$.Given the direction cosines $(l, m, n) = (-2/\sqrt{17}, 3/\sqrt{17}, -2/\sqrt{17})$ and the length $r = AB = \sqrt{17}$.The coordinates of $B$ are given by $x = x_A + lr$,$y = y_A + mr$,and $z = z_A + nr$.Substituting the values:$x = 3 + (-2/\sqrt{17}) \times \sqrt{17} = 3 - 2 = 1$$y = -6 + (3/\sqrt{17}) \times \sqrt{17} = -6 + 3 = -3$$z = 10 + (-2/\sqrt{17}) \times \sqrt{17} = 10 - 2 = 8$Thus,the coordinates of $B$ are $(1, -3, 8)$.

Class 12 Mathematics Three Dimensional Geometry System of co-ordinates, Direction cosines and direction ratios, Projection

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The direction cosines of a line segment $AB$ are $-2/\sqrt{17}, 3/\sqrt{17}, -2/\sqrt{17}$. If $AB = \sqrt{17}$ and the coordinates of $A$ are $(3, -6, 10)$,then the coordinates of $B$ are

A
$(1, -2, 4)$
B
$(2, 5, 8)$
C
$(-1, 3, -8)$
D
$(1, -3, 8)$

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System of co-ordinates, Direction cosines and direction ratios, Projection

If the direction ratios of a line are $1, -3, 2$,then the direction cosines of the line are

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Let the direction cosines of two lines satisfy the equations: $4l+m-n=0$ and $2mn+10nl+3lm=0$. Then the cosine of the acute angle between these lines is:

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Show that the three lines with direction cosines $\frac{12}{13}, \frac{-3}{13}, \frac{-4}{13} ; \frac{4}{13}, \frac{12}{13}, \frac{3}{13} ; \frac{3}{13}, \frac{-4}{13}, \frac{12}{13}$ are mutually perpendicular.

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The direction cosines of a line segment $AB$ are $-2/\sqrt{17}, 3/\sqrt{17}, -2/\sqrt{17}$. If $AB = \sqrt{17}$ and the coordinates of $A$ are $(3, -6, 10)$,then the coordinates of $B$ are

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