Let ` vec r , vec a , vec ba n d vec c` be four nonzero vectors such that ` vec rdot vec a=0,| vec rxx vec b|=| vec r|| vec b|a n d| vec rxx vec c|=| vec r|| vec c|dot` Then `[abc]` is equal to `|a||b||c|` b. `-|a||b||c|` c. `0` d. none of these

Options

A. |a||b||c|
B. `-|a||b||c|`
C. 0
D. none of these

Answer

c

Explanation

`vecr.veca = 0, |vecr xx vecb| = |vecr||vecb| and |vecr xx vecc|`
`|vecr||vecc|`
` [ veca vecb vecc] =0`