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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - d
`|(veca xx vecb).vecc|=|veca||vecb||vecc|`
`or||veca||vecb|sin theta cos alpha|=|veca||vecb||vecc|`
` or |sinstheta||cos alpha|=1`
`Rightarrow theta=pi//2 and alpha=0`
` Rightarrow veca bot vecband vecc||hatn`
or perpendicular to both `veca and vecb`
`Rightarrow veca.vecb=vecb.vecc=vecc.veca=0`

4 views Answered 2023-02-05 15:29