Direction cosines of the line frac{x+2}{2} = | vedclass

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

Question

(A) The given equation of the line is $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$. First,rewrite the line in standard symmetric form: $\frac{x+2}{2} = \f

Vedclass · Accepted Answer

$\frac{4}{5}, \frac{3}{5}, 0$

Vedclass · Answer

(A) The given equation of the line is $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$. First,rewrite the line in standard symmetric form: $\frac{x+2}{2} = \frac{y - 5/2}{3/2} = \frac{z+1}{0}$. The direction ratios of the line are $(a, b, c) = (2, 3/2, 0)$. To simplify,multiply by $2$: $(4, 3, 0)$. The magnitude of the direction vector is $\sqrt{4^2 + 3^2 + 0^2} = \sqrt{16 + 9} = \sqrt{25} = 5$. The direction cosines $(l, m, n)$ are given by $\left( \frac{a}{\sqrt{a^2+b^2+c^2}}, \frac{b}{\sqrt{a^2+b^2+c^2}}, \frac{c}{\sqrt{a^2+b^2+c^2}} \right)$. Thus,the direction cosines are $\left( \frac{4}{5}, \frac{3}{5}, 0 \right)$.

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ are $.......$

Similar Questions

If the direction ratios of a line are $1, -3, 2$,what are its direction cosines?

If a line lies in the octant $OXYZ$ and it makes equal angles with the axes,then

If $< a, b, c >$ and $< a', b', c' >$ are the direction ratios of two perpendicular lines,then which of the following is true?

If a line makes angles $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with $Y$-axis and $Z$-axis respectively,then the obtuse angle made by that line with $X$-axis is

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module