Show that the angle between two diagonal...

Show that the angle between two diagonals of a cube is `cos^(-1)sqrt(1/3)dot`

`pi/3`

`pi/4`

`cos^(-1)(1/sqrt(3))`

`cos^(-1)(1/3)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

THREE DIMENSIONAL GEOMETRY
AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - B|47 Videos
THREE DIMENSIONAL GEOMETRY
AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - C|14 Videos
THREE DIMENSIONAL GEOMETRY
AAKASH INSTITUTE ENGLISH|Exercise TRY YOURSELF|97 Videos
STRAIGHT LINES
AAKASH INSTITUTE ENGLISH|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos
TRIGNOMETRIC FUNCTIONS
AAKASH INSTITUTE ENGLISH|Exercise Section - J (Akash Challengers Question)|16 Videos

Similar Questions

Explore conceptually related problems

Show that the angle between two diagonals of a cube is cos^(-1)(1/3)dot

Find the angle between any two diagonals of a cube.

Find the angel between any two diagonals of a cube.

An ellipse is inscribed in a reactangle and the angle between the diagonals of the reactangle is tan^(-1)(2sqrt(2)) , then find the ecentricity of the ellipse

If the edges of a rectangular parallelepiped are a ,b ,c prove that the angles between the four diagonals are given by cos^(-1)((a^2+-b^2+-c^2)/(a^2+b^2+c^2))dot

In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d vec A D , angle between vec A Ba n d vec A D is 2pi//3 , 15| vec A C|=3| vec A B|=5| vec A D|dot Then the angle between vec B Aa n d vec C D is cos^(-1)(sqrt(14))/(7sqrt(2)) b. cos^(-1)(sqrt(21))/(7sqrt(3)) c. cos^(-1)2/(sqrt(7)) d. cos^(-1)(2sqrt(7))/(14)

Solve sqrt(x-1)>sqrt(3-x)dot

(i) Find the angle bewteen the lines whose direction ratios are 1, 2, 3 and - 3 , 2 , 1 (ii) Find the angle between two diagonals of a cube.

The angle between two planes x+2y+2z=3 and -5x+3y+4z=9 is (A) cos^-1(3sqrt(2))/10 (B) cos^-1 (19sqrt(2))/30 (C) cos^-1 (9sqrt(2))/20 (D) cos^-1 (3sqrt(2))/5

If veca=(3,1) and vecb=(1,2) represent the sides of a parallelogram then the angle theta between the diagonals of the paralelogram is given by (A) theta=cos^-1(1/sqrt(5)) (B) theta=cos^-1(2/sqrt(5)) (C) theta=cos^-1 (1/(2sqrt(5))) (D) theta = pi/2

AAKASH INSTITUTE ENGLISH-THREE DIMENSIONAL GEOMETRY -ASSIGNMENT SECTION - A

Find the foot of perpendicular from (0, 2, 3) to the line (x-3)/2= (...
Text Solution
|
The shortest distance between the lines (x-1)/2= (y-1)/3=(z+2)/6and ...
Text Solution
|
Show that the angle between two diagonals of a cube is cos^(-1)sqrt(1/...
Text Solution
|
The distance of a plane 3x + 4y - 5z = 60 from origin
Text Solution
|
Find the equation of line passing through (2, -1, 3) and equally incli...
Text Solution
|
The lines (x-1)/1=(y-2)/2=(z-3)/(3) and (x-1)/1=y/3 =z/4 are
Text Solution
|
The equation of the plane through the line of intersection of the plan...
Text Solution
|
Lines vecr = veca(1) + lambda vecb and vecr = veca(2) + svecb will lie...
Text Solution
|
The equation of a plane through the point (2, 3, 1) and (4, -5, 3) a...
Text Solution
|
If the line (x-4)/(1)=(y-2)/(1)=(z-k)/(2) lies exactly on the plane 2x...
Text Solution
|
The angle between diagonal of a cube and diagonal of a face of the c...
Text Solution
|
A point at a distance of sqrt(6) from the origin which lies on the s...
Text Solution
|
The point where the line through A = (3, -2, 7) and B = (13, 3, -8) ...
Text Solution
|
Find the equation of plane containing the line x+ y - z = 0 = 2x – y +...
Text Solution
|
The equation of the plane passing through the intersection of x + 2y +...
Text Solution
|
A unit vector normal to the plane through the points hati, 2hatj and...
Text Solution
|
The direction cosines of the normal to the plane x + 2y - 3z + 4 = 0...
Text Solution
|
The two lines x=ay+b,z=cy+d and x=a'y+b', z=c'y +d' are pendicular to ...
Text Solution
|
The angle between the line whose d.c.'s are connected by the relations...
Text Solution
|
Find the coordinates of the foot of perpendicular drawn from th poi...
Text Solution
|