English

Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______ - Mathematics

Advertisements
Advertisements

Question

Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.

Options

  • `(2x)/sqrt(3) = y/2 = z/0`

  • `(2x)/sqrt(3) = (2y)/1 = z/0`

  • 2x = `(2y)/sqrt(3) = z/1`

  • `(2x)/sqrt(3) = (2y)/1 = z/1`

MCQ
Fill in the Blanks
Advertisements

Solution

Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is `underlinebb((2x)/sqrt(3) = (2y)/1 = z/0)`.

Explanation:

Here, direction cosines of the line are

l = cos 30°, m = cos 60°, n = cos 90°

l = `sqrt(3)/2`, m = `1/2`, n = 0

Here, line passes through the point (0, 0, 0).

So, the required equation of line is

`(x - 0)/(sqrt(3)/2) = (y - 0)/(1/2) = (z - 0)/0`

`\implies (2x)/sqrt(3) = (2y)/1 = z/0`

shaalaa.com
  Is there an error in this question or solution?
2022-2023 (March) Outside Delhi Set 2

RELATED QUESTIONS

Find the direction cosines of the line 

`(x+2)/2=(2y-5)/3; z=-1`


If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.

(A) `0,1/sqrt2,-1/sqrt2`

(B) `0,-1/sqrt2,-1/sqrt2`

(C) `1,1/sqrt2,1/sqrt2`

(D) `0,-1/sqrt2,1/sqrt2`


Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).


Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .


Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.


Find the angle between the lines whose direction ratios are proportional to abc and b − cc − aa− b.


Find the angle between the lines whose direction cosines are given by the equations

 l + 2m + 3n = 0 and 3lm − 4ln + mn = 0


Find the angle between the lines whose direction cosines are given by the equations

2l + 2m − n = 0, mn + ln + lm = 0


What are the direction cosines of X-axis?


If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.


Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.


Write direction cosines of a line parallel to z-axis.


For every point P (xyz) on the x-axis (except the origin),


Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line `vec("r") = (-2hat"i"+3hat"j") +lambda(2hat"i"-3hat"j"+6hat"k").`Also, find the distance between these two lines.


Verify whether the following ratios are direction cosines of some vector or not

`1/5, 3/5, 4/5`


Find the direction cosines of a vector whose direction ratios are

`1/sqrt(2), 1/2, 1/2`


Find the direction cosines of a vector whose direction ratios are
0, 0, 7


Find the direction cosines and direction ratios for the following vector

`3hat"i" + hat"j" + hat"k"`


Find the direction cosines and direction ratios for the following vector

`5hat"i" - 3hat"j" - 48hat"k"`


A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians


If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`,  find the magnitude and direction cosines of `vec"a", vec"b", vec"c"`


If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.


A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.


If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.


If a line makes an angle of `pi/4` with each of y and z-axis, then the angle which it makes with x-axis is ______.


The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`


Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.


If the directions cosines of a line are k,k,k, then ______.


The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.


Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×