(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

Medium

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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THREE DIMENSIONAL GEOMETRY

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

$A$ line passes through the points $A (6, -7, -1)$ and $B (2, -3, 1)$. Find the direction cosines of the line such that the angle $\alpha$ made with the $x$-axis is acute.

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If the coordinates of the points $A, B, C, D$ are $(2, 3, -1), (3, 5, -3), (1, 2, 3)$ and $(3, 5, 7)$ respectively,then the projection of $AB$ on $CD$ is

Easy

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The obtuse angle between the lines whose direction ratios are determined by the equations $a+b+c=0$ and $2ab+2ac-bc=0$ is

MediumTS EAMCET 2020

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The angle between the straight lines,whose direction cosines are given by the equations $2l + 2m - n = 0$ and $mn + nl + lm = 0$,is:

DifficultJEE MAIN 2021

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If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

MediumAP EAMCET 2017

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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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$A$ line passes through the points $A (6, -7, -1)$ and $B (2, -3, 1)$. Find the direction cosines of the line such that the angle $\alpha$ made with the $x$-axis is acute.

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