हिंदी

If O is the Origin, Op = 3 with Direction Ratios Proportional to −1, 2, −2 Then the Coordinates of P Are (A) (−1, 2, −2) (B) (1, 2, 2) (C) (−1/9, 2/9, −2/9) (D) (3, 6, −9) - Mathematics

Advertisements
Advertisements

प्रश्न

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

विकल्प

  •  (−1, 2, −2)

  •  (1, 2, 2)

  •  (−1/9, 2/9, −2/9)

  •  (3, 6, −9)

MCQ

उत्तर

(1, 2,2)

Let the coordinates of P be (x, y, z). Then,

Direction ratios of OP= Coordinates of P Coordinates of O

1, 2, 2 = (x0), (y0), (z0)

Thus, coordinates of P are (1, 2,2).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 27: Direction Cosines and Direction Ratios - MCQ [पृष्ठ २६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 27 Direction Cosines and Direction Ratios
MCQ | Q 11 | पृष्ठ २६

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.


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 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.


Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .


Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.


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 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


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


Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).


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


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.


For every point P (xyz) on the xy-plane,

 


Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is


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


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

`4/3, 0, 3/4`


Find the direction cosines of a vector whose direction ratios are

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


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" + hat"j" + hat"k"`


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.


The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.


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


The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`


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.


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 Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.


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


Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.


If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin2α + sin2β + sin2γ will be ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×