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a.b = 0 rArrVectors a and b are orthogon...

`a.b = 0 rArr`Vectors a and b are orthogonal
(b)IF ABCD be a cyclic quadrilateral, then `A + C = (pi)/(2)` and `B + D = (pi)/(2)`
(c )`[abc] =a.(bxxc)`.
If `u = q-r, r-p, p-q and v = (1)/(a),(1)/(b),(1)/(c) ` and a,b,c are `T_(p),T_(q),T_(r)` of an HP, then the angle between the vectors u and v is .....

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The correct Answer is:
`theta = pi//2`
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a.b = 0 rArr Vectors a and b are orthogonal (b)IF ABCD be a cyclic quadrilateral, then A + C = (pi)/(2) and B + D = (pi)/(2) (c ) [abc] =a.(bxxc) . If u = q-r,r-p,p-q and v = log a^(2),log b^(2), log c^(2) and a, b, c are T_(p), T_(q), T_(s) of a G.P. then angle between vectors u and v is ...

If u = q-r,r-p,p-q and v = loga^(2), logb^(2), logc^(2) and a,b, c and T_(p), T_(q), T_(r) of a G.P. then angle between vectors u and v is ........

Knowledge Check

  • If a,b,c are in AP, p,q,r are in HP and (p/q+r/p)=(a/c+c/a), then ap, bq, cr are in

    A
    AP
    B
    GP
    C
    HP
    D
    None of these

  • In a G.P. T_(p) = a, T_(q) = b and T_(r) = c where a, b, c are +ive then angle between the vectors log a^(2)I + log b^(2)j + logc^(2)k and (q-r)i+(r-p)j+(p-q)k is :

    A
    `(pi)/(3)`
    B
    `(pi)/(2)`
    C
    `sin^(-1) ""(1)/(sqrt(suma^(2)))`
    D
    none

  • If a = 2p + 3q -r, b = p - 2q + 2r and c = -2p + q -2r, and R = 3p -q + 2r , where p, q, r are non-coplanar vectors, then R in terms of a, b, c is

    A
    `5a + 2b + 3c`
    B
    `3a + 5b + 2c`
    C
    `2a + 5b + 3c`
    D
    `5a + 3b + 2c`

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    If a^(p)=b^(q)=c^(r)=abc, then pqr=

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    If anep,bne q,cner and |(p,b,c),(a,q,c),(a,b,r)| =0 , then the value of p/(p-a)+q/(q-b)+r/(r-c) is

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