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For non- zero vectors overset(to)(a) ,...

For non- zero vectors `overset(to)(a) , overset(to)(b), overset(to)(c ),|(vec(a)xx vec(b)). vec(c )|`
`=|vec(a)||vec(b)||vec(c )|` holds if and only if

A

` overset(to)(a) , overset(to)(b)=0, overset(to)(b), overset(to)( c)=0`

B

`overset(to)(b), overset(to)(c) =0, overset(to)(c ), overset(to)(a) =0`

C

` overset(to)( c), overset(to)(a)= 0, overset(to)(a), overset(to)(b)=0`

D

` overset(to)(a).overset(to)(b)=overset(to)(b).overset(to)(c)=overset(to)(c).overset(to)(a)=0`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `|(vec(a) xx vec(b)) "." vec(c ) |=|vec(a)||vec(b)||vec(c )|`
`rArr ||vec(a) ||vec(b)| sin 0 hat(n) "." vec(c ) |=| vec(a)||vec(b)||vec(c )|`
`rArr |vec(a)||vec(b)||vec( c)|| sin 0 ". " cos alpha |=| vec(a)||vec(b)||vec(c )|`
`:. vec(a) bot vec(b) " and " vec( c)|| hat(n)`
`i.e., vec(a) bot vec(b) " and " vec(c ) ` perpendicular to both` vec(a) " and " vec(b).`
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