Angle between the vectors `vec(a)=-hat(i)+2hat(j)+hat(k)` and `vec(b)=xhat(i)+hat(j)+(x+1)hat(k)`

Options

A. is obtuse angle
B. is acute angle
C. is `90^(@)`
D. depends on x

Answer

B, D

Explanation

Angle between `vec(a)` and `vec(b)`,
`cos theta=(vec(a).vec(b))/(ab)=(-x+2+x+1)/(sqrt(1+4+1)sqrt(x^(2)+1^(2)+(x+1)^(2)))`
`=(3)/sqrt(6[x^(2)+1+(x+1)^(2)]) gt 0`