Statement 1: `veca, vecb and vecc` are three mutually perpendicular unit vectors and `vecd` is a vector such that `veca, vecb, vecc and vecd` are non- coplanar. If `[vecd vecb vecc] = [vecdvecavecb] = [vecdvecc veca] = 1, " then " vecd= veca+vecb+vecc`
Statement 2: `[vecd vecb vecc] = [vecd veca vecb] = [vecdveccveca] Rightarrow vecd` is equally inclined to `veca, vecb and vecc`. Option A: Both the statements are true and statement 2 is the correct explanation for statement 1. Option B: Both statements are true but statement 2 is not the correct explanation for statement 1. Option C: Statement 1 is true and Statement 2 is false Option D: Statement 1 is false and Statement 2 is true.

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

Let `vced = lamda_(1) veca + lambda_(2) vecb +lambda_(3) vecc`
`Rightarrow [vecdvecavecb] = lamda_(3)[veccvecavecb]Rightarrowlambda_(3)=1`
`[veccveca vecb] =1` (because `veca vecb and vecc` are three mutually perpendicular unit vectors)
similarly, `lambda_(1) = lambda_(2) =1`
`Rightarrow vecd =veca +vecb +vecc`
Hence, statement 1 and statement 2 are correct , but statement 2 does not explain statement 1 as it does not give the value of dot products.