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vec(a) and vec(b) are non-zero vectors s...

`vec(a) and vec(b)` are non-zero vectors such that `vec(a) xx vec(b)= vec(b) xx vec(a)` " then" `vec(a), vec(b)` are

A

this result is always true

B

this result is impossible

C

parallel to each other

D

perpendicular to each other

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • The vector vec(a) xx (vec(b) xx vec(a)) is

    A
    Perpendicular to `vec(a)`
    B
    Perpendicular to `vec(b)`
    C
    Null vector
    D
    Perpendicular to both `vec(a) and vec(b)`

  • If vec(a) and vec(b) are unit vectors such that |vec(a) xx vec(b)|=1 , then the angle between vec(a) and vec(b) is

    A
    `pi//4`
    B
    `pi//2`
    C
    `pi//3`
    D
    `pi`

  • The vectors vec(a) and vec(b) are not perpendicular and vec(c ) and vec(d) are two vectors satisfying vec(b) xx vec(c )= vec(b) xx vec(d) and vec(a).vec(d)= 0 . Then the vector vec(d) is equal to

    A
    `vec(b)+ ((vec(b).vec(c ))/(vec(a).vec(b))) vec(c )`
    B
    `vec(b) + ((vec(b).vec(c ))/(vec(a).vec(b))) vec(c )`
    C
    `vec(b)- ((vec(b).vec(c ))/(vec(a).vec(b))) vec(c )`
    D
    `vec(c )-((vec(a).vec(c ))/(vec(a).vec(b))) vec(b)`

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