If a line has the direction ratios -18, 12, - | vedclass

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

Question

(A) Given direction ratios are $a = -18, b = 12, c = -4.$The magnitude of the vector is $\sqrt{a^2 + b^2 + c^2} = \sqrt{(-18)^2 + (12)^2 + (-4)^2}.$$=

Vedclass · Accepted Answer

$\frac{-9}{11}, \frac{6}{11}, \frac{-2}{11}$

Vedclass · Answer

(A) Given direction ratios are $a = -18, b = 12, c = -4.$The magnitude of the vector is $\sqrt{a^2 + b^2 + c^2} = \sqrt{(-18)^2 + (12)^2 + (-4)^2}.$$= \sqrt{324 + 144 + 16} = \sqrt{484} = 22.$The direction cosines $(l, m, n)$ are given by $\frac{a}{\sqrt{a^2+b^2+c^2}}, \frac{b}{\sqrt{a^2+b^2+c^2}}, \frac{c}{\sqrt{a^2+b^2+c^2}}.$$l = \frac{-18}{22} = \frac{-9}{11},$$m = \frac{12}{22} = \frac{6}{11},$$n = \frac{-4}{22} = \frac{-2}{11}.$Thus,the direction cosines are $\frac{-9}{11}, \frac{6}{11}, \frac{-2}{11}.$

If a line has the direction ratios $-18, 12, -4,$ then what are its direction cosines?

Similar Questions

$A$ line which makes an angle of $60^o$ with the $y$-axis and $z$-axis,then the angle which it makes with the $x$-axis is ......... $^o$.

If the direction ratios of two lines are $5, -12, 13$ and $-3, 4, 5$,then the angle between them is:

Which of the following can not be the direction cosines of a line?

If a line makes angles $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $X, Y$ and $Z$ axis respectively,then its direction cosines are

The direction cosines of the line making angles $\frac{\pi}{4}, \frac{\pi}{3}$ and $\theta$ $(0 < \theta < \frac{\pi}{2})$ respectively with $X, Y$ and $Z$ axes are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module