Home
Class 12
MATHS
The edges of a parallelopiped are of uni...

The edges of a parallelopiped are of unit length and a parallel to non-coplanar unit vectors `hata, hatb, hatc` such that `hata.hatb=hatb.hatc=hatc.veca=1//2`. Then the volume of the parallelopiped in cubic units is

Text Solution

Verified by Experts

Since information are given in terms of `hata.hatb,hatb.ahtc,hat c.hata`
`[hata hatb hatc]^(2)=(Volume)^(2)=|{:(hata.hata,hata.hatb,hata.hatc),(hatb.hata,hatb.hatb,hatb.hatc),(hatc.hata,hatc.hatb,hatc.hatc):}|`
`=|{:(1,(1)/(2),(1)/(2)),((1)/(2),1,(1)/(2)),((1)/(2),(1)/(2),1):}|`
`=(1)/(2)`
`:.` Volume `(1)/(sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    AAKASH INSTITUTE|Exercise ILLUSTRATION|1 Videos

  • VECTOR ALGEBRA

    AAKASH INSTITUTE|Exercise TRY YOURSELF|20 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

The edges of a parallelopiped are of unit length and are parallel to non coplanar unit vectors hata,hatb,hatc such that hata.hatb=hatb.hatc=hatc.hata=1/2 Then the volume of the parallelopiped is (A) 1/sqrt(2) (B) 1/(2sqrt(2)) (C) sqrt(3)/2 (D) 1/sqrt(3)

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors vec a, vec b, vec c such that hat a.hatb=hatb .hatc=hatc.hata=1/2. Then, the volume of parallelopiped is

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors hat(a), hat(b), hat(c) such that hat(a)*hat(b)=hat(b)*hat(c)=hat(c)*hat(a)=(1)/(2). Then, the volume of the parallelopiped is

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors hat(a), hat(b), hat(c ) such that hat(a).hat(b)=hat(b).hat(c )=hat(c ).hat(a)=(1)/(3) . Then, the volume of the parallelopiped is :-

The edges of a parallelopiped of unit length are parallal to non-coplanar unit vectors widehat a,hat b,hat c such that widehat a.hat b=hat b*hat c=hat c.widehat a=1/2, then the volume of parallelopiped whose edges are widehat a xxhat b,hat b xxhat chat c xx widehat a is

The deges of a parallelopied are of unit length and are parallel to non- coplanar unit vector hat(a), hat(b) , hat(c ) such that hat(a) , hat(b) = hat(b), hat( c)=hat(c ), hat(a) = .(1)/(2). Then the volume of the parallelopiped is

If vectors hata, hatb, hatc are in space such that hata.hatb=hatb.hatc=hatc.hata=1/2 , then (hataxxhatb).(hataxx(hatbxxhatc)) is equal to

If hata, hatb, hatc are unit vectors such that hata+hatb+hatc=0 then find the value of hata.hatb+hatb.hatc+hatc.hata