मराठी

If a line makes angles π2,34π and π4 with x, y, z axis, respectively, then its direction cosines are ______.

Advertisements
Advertisements

प्रश्न

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

रिकाम्या जागा भरा
Advertisements

उत्तर

If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are `+- (- 1/sqrt(2) 1/sqrt(2))`.

Explanation:

The direction cosines are `cos  pi/2, cos  3/4 pi, cos  pi/4`

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Introduction to Three Dimensional Geometry - Solved Examples [पृष्ठ २३३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 12 Introduction to Three Dimensional Geometry
Solved Examples | Q 20 | पृष्ठ २३३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Three vertices of a parallelogram ABCD are A (3, –1, 2), B (1, 2, –4) and C (–1, 1, 2). Find the coordinates of the fourth vertex.


If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (–4, 3b, –10) and R (8, 14, 2c), then find the values of a, b and c.


Name the octants in which the following points lie: (5, 2, 3)


Name the octants in which the following points lie: 

 (7, 4, –3)


Name the octants in which the following points lie: 

(–5, –3, –2) 


Find the image  of: 

 (–2, 3, 4) in the yz-plane.


Planes are drawn through the points (5, 0, 2) and (3, –2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed. 


The coordinates of a point are (3, –2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.


Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.


Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle. 


Are the points A(3, 6, 9), B(10, 20, 30) and C(25, –41, 5), the vertices of a right-angled triangle?


Verify the following: 

 (0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle. 


Verify the following: 

(0, 7, 10), (–1, 6, 6) and (–4, 9, –6) are vertices of a right-angled triangle.


Verify the following: 

 (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram.


Find the locus of the points which are equidistant from the points (1, 2, 3) and (3, 2, –1).


Write the distance of the point P (2, 3,5) from the xy-plane.


Write the distance of the point P(3, 4, 5) from z-axis.


Write the coordinates of the foot of the perpendicular from the point (1, 2, 3) on y-axis.


What is the locus of a point for which y = 0, z = 0?


Find the point on y-axis which is at a distance of  \[\sqrt{10}\] units from the point (1, 2, 3).


XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio


The perpendicular distance of the point P (6, 7, 8) from xy - plane is


Find the co-ordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1).


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 the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane


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 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 + δn2


Find the foot of perpendicular from the point (2,3,–8) to the line `(4 - x)/2 = y/6 = (1 - z)/3`. Also, find the perpendicular distance from the given point to the line.


Find the length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.


The plane ax + by = 0 is rotated about its line of intersection with the plane z = 0 through an angle α. Prove that the equation of the plane in its new position is ax + by `+- (sqrt(a^2 + b^2) tan alpha)z ` = 0


The sine of the angle between the straight line `(x - 2)/3 = (y - 3)/4 = (z - 4)/5` and the plane 2x – 2y + z = 5 is ______.


The locus represented by xy + yz = 0 is ______.


The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to ______.


The line `vecr = 2hati - 3hatj - hatk + lambda(hati - hatj + 2hatk)` lies in the plane `vecr.(3hati + hatj - hatk) + 2` = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×