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Let O be the origin and vec(OX) , vec(O...

Let O be the origin and` vec(OX) , vec(OY) , vec(OZ)` be three unit vector in the directions of the sides `vec(QR) , vec(RP),vec(PQ)` respectively , of a triangle PQR.
`|vec(OX)xxvec(OY)|=`

A

sin (P + Q)

B

sin 2R

C

sin (P+R)

D

sin (Q+R)

Text Solution

Verified by Experts

The correct Answer is:
A
`|vec(OX)xxvec(OY)|=|vec(OX)||vec(OY)|sin (pi-R)`
`=sin R=sin (P+Q)`
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Knowledge Check

  • Let O be the origin , and vec(OX),vec(OY),vec(OZ) be three unit vector in the directions of the sides vec(OR) , vec(RP) , vec(PQ) respectively, of a triangle PQR, Then , |vec(OX) xx vec(OY)| =

    A
    sin ( P +Q)
    B
    sin 2R
    C
    sin (P +R)
    D
    sin (Q +R)

  • The unit vector bisecting vec(OY) and vec(OZ) is

    A
    `(veci+vecj+veck)/sqrt(3)`
    B
    `(veci-veck)/sqrt(2)`
    C
    `(vecj+veck)/sqrt(2)`
    D
    `(-vecj+veck)/sqrt(2)`

  • Let vec(p),vec(q),vec(r) be three unit vectors such that vec(p)xxvec(q)=vec(r) . If vec(a) is any vector such that [vec(a)vec(q)vec(r )]=1,[vec(a)vec(r)vec(p )]=2 , and [vec(a)vec(p)vec(q )]=3 , then vec(a)=

    A
    `vec(p)+3q+vec(r )`
    B
    `vec(3p)+vec(2q)+vec(r )`
    C
    vec(p)-vec(2q)-vec(3r)`
    D
    `vec(p)+vec(2q)+vec(3q)`

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