`x` के किन मानो के लिए, दो सदिश `(x^(2)-1)hati+(x+2)hatj+x^(2)hatk` और `2hati-xhatj+3hatk` परस्पर लम्ब है

Options

A. `0`
B. `1`
C. `-1`
D. `1//2`

Answer

B

Explanation

दो सदिश `a=(x^(2)-1)+(x+2)hatj+x^(2)hatk` तथा `b=2hati-xhatj+3hatk` लंबकोणीये होंगे, यदि `a.b=0`
`Rightarrow 2(x^2-1)-x(x+2)+3x^(2)=0`
`Rightarrow 2x^(2)-2-x^(2)-2x+3x^(2)=0 Rightarrow 4x^(2)-2x-2=0`
`Rightarrow 2x^(2)-x-1=0 Rightarrow (2x+1)(x-1)=0`
`therefore x=1" "[therefore x ne (-1)/(2)]`