मराठी

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. - Mathematics

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.

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Three Dimensional Geometry - Exercise 11.4 [पृष्ठ ४९७]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 11 Three Dimensional Geometry
Exercise 11.4 | Q 2 | पृष्ठ ४९७

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

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).


Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 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).


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


What are the direction cosines of X-axis?


What are the direction cosines of Z-axis?


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


Write the coordinates of the projection of point P (xyz) on XOZ-plane.


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


Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(abc) from 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.


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


The direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 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

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


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

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


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

`4/3, 0, 3/4`


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

`hat"i" - hat"k"`


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


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.


O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.


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


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


The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are ______.


Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×