मराठी

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.

बेरीज
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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Three Dimensional Geometry - Solved Examples [पृष्ठ २२५]

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Write the direction ratios of the following line :

`x = −3, (y−4)/3 =( 2 −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`


If l1m1n1 and l2m2n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1n1l2 − n2l1l1m2 ­− l2m1.


Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`


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.


If the coordinates of the points ABCD are (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2), then find the angle between AB and CD.


Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.


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

2l − m + 2n = 0 and mn + nl + lm = 0


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


Write the distance of the point (3, −5, 12) from X-axis?


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


Write the distance of the point P (xyz) from XOY plane.


Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.


Find the distance of the point (2, 3, 4) from the x-axis.


If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.


A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is


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


If O is the origin, OP = 3 with direction ratios proportional to −1, 2, −2 then the coordinates of P are


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


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


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

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


Find the direction cosines and direction ratios for the following vector

`3hat"i" - 3hat"k" + 4hat"j"`


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


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


If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.


If a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.


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 ______.


What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.


The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×