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For non zero vectors veca,vecb, vecc |...

For non zero vectors `veca,vecb, vecc`
`|(vecaxxvecb).vec|=|veca||vecb||vecc|` holds iff

A

`veca.vecb=vecb.vecc=veca.veca=0`

B

`veca.vecb=0=vecb.vecc`

C

`vecb.vecc=0=vecc.veca`

D

`vecc.veca=0=veca.vecb`

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For non zero vectors veca,vecb,vecc|(vecaxxvecb).vecc|=|veca||vecb||vec| holds if and only if (A) veca.vecb=0,vecb.vecc=0 (B) vecb.vecc=0,vecc.veca=0 (C) vecc.veca=0,veca.vecb=0 (D) veca.vecb=vecb.vecc=vecc.veca=0

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Knowledge Check

  • For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc = |veca||vecb||vecc| holds if and only if

    A
    `veca.vecb=0 , vecb .vecc=0`
    B
    `vecb.vecc = 0, vecc, veca =0`
    C
    `vecc.veca =0, veca,vecb =0`
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  • Statement 1: If V is the volume of a parallelopiped having three coterminous edges as veca, vecb , and vecc , then the volume of the parallelopiped having three coterminous edges as vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc is V^(3) Statement 2: For any three vectors veca, vecb, vecc |(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)

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