मराठी

A Rectangular Parallelopiped is Formed by Planes Drawn Through the Points (5, 7, 9) . the Length of an Edge of this Rectangular Parallelopiped is (A) 2 (B) 3 (C) 4 (D) All of These

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • 2

  • 3

  • 4

  • all of these

MCQ
बेरीज
Advertisements

उत्तर

all of these

The given points (5, 7, 9) and (2, 3, 7) are two diagonally opposite vertices of the parallelopiped as all of their coordinates are different

 Edges of the parallelopiped = |52|, |73|, |97|                                                      =3, 4, 2

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 26: Direction Cosines and Direction Ratios - MCQ [पृष्ठ २५]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 26 Direction Cosines and Direction Ratios
MCQ | Q 3 | पृष्ठ २५

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Find the direction cosines of the line 

`(x+2)/2=(2y-5)/3; z=-1`


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`


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


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


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


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


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.


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


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


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 inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.


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 the point P (2, −3, 5) on Y-axis.


Write direction cosines of a line parallel to 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


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


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


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.


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"`


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


If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`,  find the magnitude and direction cosines of `vec"a", vec"b", vec"c"`


If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.


P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.


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 line makes an angle of `pi/4` with each of y and z-axis, then the angle which it makes with x-axis is ______.


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


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 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.


Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.


Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.


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×