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

The length of the projection of the line segment joining the points $(3, 4, 5)$ and $(4, 6, 3)$ on the line joining the points $(-1, 2, 4)$ and $(1, 0, 5)$ is

Which of the following statements is false?

If a line makes an angle of $\frac{\pi}{4}$ with the positive directions of each of the $x$-axis and $y$-axis,then the angle that the line makes with the positive direction of the $z$-axis is

If the projections of a line segment on the coordinate axes are $3, 4,$ and $5$,then its length is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module