Home
Class 10
PHYSICS
Show that a.(bxxc) is equal in magnitude...

Show that `a.(bxxc)` is equal in magnitude to the volume of the parallelopiped formed on the three vectors a, b and c.

Text Solution

Verified by Experts

Let a parallelopiped be formed on threevectors ` vec(OA) = vec a, vec(OB) = vecb, vec(OC) = vecc`
Now, `vecbxxvecc = bc sin 90^@ hatn = bc hatn`

where `hatn` is the unit vector along `bar(OA)` perpendicular to the plane containing ` vecb " and " vecc`
Nom, ` veca.(vecbxx vecc) a veca. bc hatn = (a)(bc)cos 0^@ = abc`
Which is equal is magnitude to the volume of parallelopiped .
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SYSTEM OF PARTICLES AND ROTATIONAL MOTION

    VGS PUBLICATION-BRILLIANT|Exercise LONG ANSWER QUESTIONS|5 Videos

  • SOUND

    VGS PUBLICATION-BRILLIANT|Exercise WORKED OUT EXAMPLES|2 Videos

  • THERMODYNAMICS

    VGS PUBLICATION-BRILLIANT|Exercise LONG ANSWER QUESTIONS|4 Videos

Similar Questions

Explore conceptually related problems

Show that a(bxxc) is equal in magnitude to the volume of the parallelepiped formed on the three vectors a, b and c.

Show that a.(bxxc) is equal in magnitude to the volume of the parallelepiped formed on the three vectors a, b and c.

Knowledge Check

  • If the volume of the tetrahedron formed by the cotermionus edges a, b and c is 4, then the volume of the parallelopiped formed by the coterminous edges a xx b, b xx c and c xx a is

    A
    576
    B
    48
    C
    16
    D
    144

  • If the volume of the tetrahedron formed by the coterminous edges bara, barb and barc is 4, then the volume of the parallelopiped formed by the coterminous edges bara xx barb, barb xx barc and barc xx bara is

    A
    144
    B
    16
    C
    48
    D
    576

  • Let a = 2 hati + hatj - 3 hatk and b - hati + 3 hatj + 2 hatk . then the volume of the parallelopiped having coterminous edges as a,b, and c where c is the vector perpendicular to the plane of a,b and |c|=2 is

    A
    `2sqrt(195)`
    B
    `24`
    C
    `sqrt(200)`
    D
    `sqrt(195)`

    • Similar Questions

    Explore conceptually related problems

    Read each statement below carefully and state with reasons, if it is true of false : (a) The magnitude of a vector is always a scalar, (b) each component of a vector is always a scalar, (c) the total path length is always equal to the magnitude of the displacement vector of a particle, (d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) three vectors not lying in a plane can never add up to give a null vector.

    The three concurrent edges of a parallelopiped represents the vectors bara, barb, barc such that [bara barb barc] = lamda . Then the volume of the parallelopiped whose three concurrent ed2es are the three concurrent diagonals of three faces of the given parallelopiped is

    Let a, b, c be three non-coplanar vectors and a^(')=(b times c)/([abc]), b^(')=(c times a)/([abc]), c^(')=(a times b)/([abc]) . The length of the altitude of the parallelopiped formed by a a^('), b^('), c^(') as coterminous edges, with respect to the base having a^(') " and "c^(') as its adjacent sides is

    If the dot product of two vectors is equal to the magnitude of the cross product of the same vectors, then the angle between the vectors is

    If the dot product of two vectors is equal to the magnitude of the cross product of the same vectors, then the angle between the vectors is

    Home
    Profile