Home
Class 12
MATHS
If the edges of a rectangular parallelop...

If the edges of a rectangular parallelopiped are 3, 2, 1 then the angle between a pair of diagonals is given by

Text Solution

Verified by Experts

`D_1=3hati+2hatj+hatk`
`D_2=-3hati+2hatj+hatk`
`D_3=3hati-2hatj+hatk`
`D_4=3hati+2hatj-hatk`
`theta=cos^(-1)(veca*vecb)/(|veca||vecb|)`
`theta_(D_1D_2)=cos^(-1)(-4/14)`
`=cos^(-1)(-2/7)`
`theta_1(D_1D_3)=cos^(-1)(3/7)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If the edges of rectangular parllelopiped are 3,2,1 then the angle between two diagonals out of 4 diagonals id

If the edges of a rectangular parallelopiped are of lengths a, b, c, then the angle between four diagonals are cos^-1((+- a^2 +-b^2 +- c^2)/(a^2+ b^2 + c^2)) .

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

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

If the edges of a rectangular parallelopiped are a, b and c, show that the angles between the four diagonals are given by cos^-1frac{a^2+-b^2+-c^2}{a^2+b^2+c^2}

Among the length, breadth and height of a rectangular parallelopiped, the length of its diagonal is the greatest.

veca=3hati-4hatj-4hatk,vec b=3hati+hatj+3hatk and vec c=hati-2hatj+hatk are three edges of a rectangular parallelopiped, prove that the volume of the parallelopiped is 49 cu unit.

If the sum of the length, breadth and height of a rectangular parallelopiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is