1.

If a=hati-hatk, b=xhati+hatj=(1-x)hatk and c=yhati+xhatj+(1+x-y)hatk. Then, [ab c ] depends on

Answer»

Only X
Only y
Both x and y
Neither x nor y

Solution :GIVEN vectors are
`a = hati - HATK , b = x hati + hatj + (1-x) hatk`
and `c = y hati + x hatj + (1+x-y) hatk`
Now, `[ABC] = |{:(1,0,-1),(x,1,1-x),(y,x,1+x-y):}|`
On applying `C_(3) rarr C_(3) + C_(1)`, we get
`= |{:(1,0,0),(x,1,1),(y,x,1+x):}|`
Thus, [a,b,c] dependsupon neither x nor y.


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