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The vector sum of two forces is perpendi...

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces :

A

are equal to each other in magnitude

B

are not equal to each other in magnitude

C

cannot be predicted

D

are perpendicular to each other

Text Solution

Verified by Experts

The correct Answer is:
A
Let `vec(F_(1))` and `vec(F_(2))` br the two forces. Then
`vec(F_(s))=vec(F_(1)) + vec(F_(2))` and `vec(F_(d))=vec(F_(1))-vec(F_(2))`
Now `vec(F_(s))` is `bot`r to `vec(F_(d)):.vec(F_(s)).vec(F_(d))=0`
or `|vec(F_(1))|^(2)=|vec(F_(2))|^(2)` or `|vec(F_(1))|=|vec(F_(2))|`
The forces are equal in magnitude.
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Knowledge Check

  • If vec a and vec b are two perpendicular vectors then

    A
    `(vec a + vec b)^(2) = vec a^(2) + vec b^(2)`
    B
    `(vec a - vec b)^(2) = vec a^(2) + vec b^(2)`
    C
    `(vec a + vec b)^(2) = (vec a- vec b)^(2)`
    D
    All of the above

  • If veca, vecb, vecc are three non-zero vector such that each one of then is perpendicular to the sum of the other two vectors, then the value of |veca+vecb+vecc|^(2) is :

    A
    `|veca|+|vecb| +|vecc|`
    B
    `2 (|veca|^(2) + |vecb|^(2) |vecc|^(2))`
    C
    `1/2(|veca|^(2) + |vecb|^(2) |vecc|^(2))`
    D
    `|veca|^(2)+|vecb|^(2) +|vecc|^(2) `

  • If veca , vecb,vecc are three non zero vectors such that each one of then is perpendicular to the sum of the other two vectors then the value of |veca+vecb+vecc|^(2) is

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    B
    `|veca|+|vecb+|+|vec c|`
    C
    `2(|veca|^(2)+|vecb+|^(2)+|vec c|^(2))`
    D
    `1/2(|veca|^(2)+|vecb+|^(2)+|vec c|^(2))`

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