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Statement 1: vec a , vec b ,a n d vec c...

Statement 1: ` vec a , vec b ,a n d vec c` are three mutually perpendicular unit vectors and ` vec d` is a vector such that ` vec a , vec b , vec ca n d vec d` are non-coplanar. If `[ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c`. Statement 2: `[ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]`; then `vec d` equally inclined to `vec a`,`vec b` and `vec c`.

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.

Text Solution

Verified by Experts

The correct Answer is:
b
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.
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