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If overset(to)(a) =hat(i) - hat(k) , o...

If `overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + hat(j) + (1-x) hat(k)` and
`vec(c ) =y hat(i) +x hat(j) + (1+x-y) hat(k) . "Then " [overset(to)(a) , overset(to)(b) , overset(to)( c) ]` depends on

A

only x

B

only y

C

neither x nor y

D

both x and y

Text Solution

Verified by Experts

The correct Answer is:
C
`[vec(a) , vec(b) , vec(c ) ] = |{:(1,,0,,-1),(x,,1,,1-x),(y,,x,,1+x-y):}|`
Applying `C_(3) to C_(1)+ C_(3),`
`|{:(1,,0,,0),(x,,1,,1),(y,,x,,1+x):}|=1`
Therefore it neither depends on x nor y.
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