हिंदी

If L1, M1, N1 And L2, M2, N2 Are the Direction Cosines of Two Mutually Perpendicular Lines, Show that the Direction Cosines of the Line Perpendicular to Both of These Are M1n2 − M2n1, N1l2 − N2l1, L1m2 ­− L2m1.

Advertisements
Advertisements

प्रश्न

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.

Advertisements

उत्तर

It is given that l1m1n1 and l2m2n2 are the direction cosines of two mutually perpendicular lines. Therefore,

Let lmn be the direction cosines of the line which is perpendicular to the line with direction cosines l1m1n1 and l2m2n2

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Three Dimensional Geometry - Exercise 11.4 [पृष्ठ ४९७]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 11 Three Dimensional Geometry
Exercise 11.4 | Q 2 | पृष्ठ ४९७

संबंधित प्रश्न

Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........


Which of the following represents direction cosines of the line :

(a)`0,1/sqrt2,1/2`

(b)`0,-sqrt3/2,1/sqrt2`

(c)`0,sqrt3/2,1/2`

(d)`1/2,1/2,1/2`


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 a line has the direction ratios −18, 12, −4, then what are its direction cosines?


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


If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.


If a line makes angles of 90°, 60° and 30° with the positive direction of xy, and z-axis respectively, find its direction cosines


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


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 angle between the lines whose direction cosines are given by the equations
(i) m + n = 0 and l2 + m2 − n2 = 0


What are the direction cosines of Y-axis?


What are the direction cosines of Z-axis?


Write the distances of the point (7, −2, 3) from XYYZ and XZ-planes.


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 ratio in which the line segment joining (abc) and (−a, −c, −b) is divided by the xy-plane.


If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?


Write direction cosines of a line parallel to z-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.


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


Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) . 


Find the direction cosines and direction ratios for the following vector

`hat"j"`


Find the direction cosines and direction ratios for the following vector

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


Find the direction cosines and direction ratios for the following vector

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


If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a


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.


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


The area of the quadrilateral ABCD, where A(0,4,1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.


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


If a line makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.


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


If the equation of a line is x = ay + b, z = cy + d, then find the direction ratios of the line and a point on the line.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×