Let f→(t)=[t]i^+(t−[t])j^+[t+1]k^ where [.] denotes the greatest integer function. Then the vectors f→54 and f→(t),0<t<1 is
parallel to each other
perpendicular to each other
inclined at cos−1271−t2
inclined at cos−18+t91+t2
f→54=54i^+54−54j^+54+1k^=i^+54−1j^+2k^=i^+14j^+2k^
when 0<t<1,f→(t)=0i→+{t−0}j→+k→ =tj→+k→so, cosθ=2+t4i→+14j→+2k→|tj→+k→|f→54⋅f→(t)=2+t4=2+t41+116+41+t2=8+t91+t2