If the projections of a line on the coordinat | vedclass

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

Question

(A) The projections of a line on the coordinate axes are the direction ratios of the line,denoted as $a = 4$,$b = 6$,and $c = 12$.To find the directio

Vedclass · Accepted Answer

$\frac{2}{7}, \frac{3}{7}, \frac{6}{7}$

Vedclass · Answer

(A) The projections of a line on the coordinate axes are the direction ratios of the line,denoted as $a = 4$,$b = 6$,and $c = 12$.To find the direction cosines $(l, m, n)$,we use the formula $l = \frac{a}{\sqrt{a^2 + b^2 + c^2}}$,$m = \frac{b}{\sqrt{a^2 + b^2 + c^2}}$,and $n = \frac{c}{\sqrt{a^2 + b^2 + c^2}}$.First,calculate the magnitude: $\sqrt{4^2 + 6^2 + 12^2} = \sqrt{16 + 36 + 144} = \sqrt{196} = 14$.Now,calculate the direction cosines:$l = \frac{4}{14} = \frac{2}{7}$$m = \frac{6}{14} = \frac{3}{7}$$n = \frac{12}{14} = \frac{6}{7}$Thus,the direction cosines are $(\frac{2}{7}, \frac{3}{7}, \frac{6}{7})$.

If the projections of a line on the coordinate axes are $4, 6, 12$,what are the direction cosines of the line?

Similar Questions

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

If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of $X, Y$ and $Z$-axes respectively,then the value of $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=$

Which of the following conditions is satisfied by a point lying on the $z$-axis?

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

If a directed line makes angles $45^{\circ}$ and $60^{\circ}$ with the $X$ and $Y$-axes respectively,then the obtuse angle $\theta$ made by the line with the $Z$-axis is (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module