Let `vecr` be a non - zero vector satisfying `vecr.veca = vecr.vecb =vecr.vecc =0` for given non- zero vectors `veca vecb and vecc`
Statement 1: `[ veca - vecb vecb - vecc vecc- veca] =0`
Statement 2: `[veca vecb vecc] =0`

Options

A. Both the statements are true and statement 2 is the correct explanation for statement 1.
B. Both statements are true but statement 2 is not the correct explanation for statement 1.
C. Statement 1 is true and Statement 2 is false
D. Statement 1 is false and Statement 2 is true.

Answer

b

Explanation

`vecr.veca= vecr.vecb= vecr.vecc=0 ` only if `veca,vecb and vecc` are coplanar, thus,
`[veca vecb vecc] =0`
Hence, statement 2 is true
Also `[veca -vecb vecb-vecc vecc-veca]=0 " even " if [veca vecb vecc] ne 0`
Hence, statement 2 is not the correct explanation for statement 1.