The direction cosines of a line segment AB ar | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 =

Vedclass · Accepted Answer

$(1, -3, 8)$

Vedclass · Answer

(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}) 	imes \sqrt{17} = 3 - 2 = 1$$y = -6 + (3/\sqrt{17}) 	imes \sqrt{17} = -6 + 3 = -3$$z = 10 + (-2/\sqrt{17}) 	imes \sqrt{17} = 10 - 2 = 8$Thus,the coordinates of $B$ are $(1, -3, 8)$.

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

Similar Questions

The projection of the point $(a, b, c)$ on the $yz$-plane is:

$A$ line makes an angle $\theta$ with the $X$ and $Z$ axes and an angle $\beta$ with the $Y$ axis. If $\sin^2 \beta = 3 \sin^2 \theta$,then $\cos^2 \theta = \dots$

The angle between the lines whose direction cosines $(\ell, m, n)$ satisfy the equations $\ell+m+n=0$ and $\ell^2+m^2-n^2=0$ is:

The angle between the pair of lines with direction ratios $1, 1, 2$ and $\sqrt{3}-1, -\sqrt{3}-1, 4$ is $... ^\circ$.

The direction cosines of the line joining the points $(-2, 4, -5)$ and $(1, 2, 3)$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module