हिंदी

If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines. - Mathematics

Advertisements
Advertisements

प्रश्न

If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.

योग
Advertisements

उत्तर

The direction cosines of a line which makes an angle of α, β, γ with the axes, are cosα, cosβ, cosγ

Therefore, D.C.’s of the line are cos30°, cos60°, cos90°

i.e., `+(sqrt(3)/2, 1/2, 0)`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Three Dimensional Geometry - Solved Examples [पृष्ठ २२५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 11 Three Dimensional Geometry
Solved Examples | Q 3 | पृष्ठ २२५

संबंधित प्रश्न

Write the direction ratios of the following line :

`x = −3, (y−4)/3 =( 2 −z)/1`


If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.


Find the direction cosines of the sides of the triangle whose vertices are (3, 5, −4), (−1, 1, 2) and (−5, −5, −2).


Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).


Define direction cosines of a directed line.


What are the direction cosines of X-axis?


What are the direction cosines of Y-axis?


What are the direction cosines of Z-axis?


A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.


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


If a unit vector  `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with }  \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.


The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)


If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is


If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio


 Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines


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.


Find the direction cosines of a vector whose direction ratios are
1, 2, 3


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" - 4hat"j" + 8hat"k"`


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"`


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 `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 `3vec"a"- 2vec"b"+ 5vec"c"`


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


Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).


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 variable line in two adjacent positions has direction cosines l, m, n and l + δl, m + δm, n + δn, show that the small angle δθ between the two positions is given by δθ2 = δl2 + δm2 + δn


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


The line `vec"r" = 2hat"i" - 3hat"j" - hat"k" + lambda(hat"i" - hat"j" + 2hat"k")` lies in the plane `vec"r".(3hat"i" + hat"j" - hat"k") + 2` = 0.


Find the direction cosine of a line which makes equal angle with coordinate axes.


If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.


The d.c's of a line whose direction ratios are 2, 3, –6, are ______.


If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×