Question

Find the maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`

Answer 1

`"Let "Delta = |(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`

Applying R2 → R2 - R1 and R3 → R3 - R1, we get

`Delta=|(1,1,1),(0,sintheta,0),(0,0,costheta)|`

`Delta=sinthetacostheta`

`Delta=(sin2theta)/2`

We know that -1 ≤ sin2θ ≤ 1

∴ Maximum value of `Delta =1/2 xx 1 = 1/2`