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If a, b, c are different real numbers an...

If `a, b, c` are different real numbers and `a hati+bhatj+chatk:bhati+chatj+a hatk & chati+a hatj+bhatk` are of three non-collinear points `A, B & C` then-

A

centroid of triangle ABC is `(a+b+c)/(3) (hat(i) + hat(j) + hat(k))`

B

`hat(i) + hat(j) + hat(k)` is equally inclined to the three vectors

C

perpendicular from the origin to the plane of triangle ABC meet at centroid

D

triangle ABC is an equilateral triangle.

Text Solution

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The correct Answer is:
A, B, C, D
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Knowledge Check

  • Let a, b and c be distinct non-negative numbers. If vectos a hati +a hatj +chatk, hati + hatk and chati +chatj+bhatk are coplanar, then c is

    A
    the arithmetic mean of a and b
    B
    the geometric mean of a and b
    C
    the harmonic mean of a and b
    D
    equal to zero

  • IF a,b,c are three real numbers not all equal and the vectors barx=ahati+bhatj+chatk,bary=bhati+chatj+ahatk,barz=c hati+ahatj+bhatk are coplanar then barx.bary+bary.barz+barz.barx is necessarily……

    A
    positive
    B
    non-negative
    C
    non-positive
    D
    negative

  • If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

    A
    `3hati-4hatj`
    B
    `3hati+4hatj`
    C
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    D
    `4hati+4hatj`

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