Question

已知在ΔABC中,AB=2,AC=3,∠BAC=θ,若向量BC=3向量BD,则向量AD*向量BC取值范围

Answer 1

IABI=2,IACI=3,

向量AB*AC=|AB|*|AC|cosθ=6cosθ,

BC=AC-AB,

∴向量AD*BC=（AB+BD）*BC=（AB+BC/3）*BC

=AB*BC+BC*BC/3=AB*（AC-AB）+(1/3)(AC-AB)^2

=AB*AC-AB^2+(1/3)(AC^2-2AC*AB+AB^2)

=6cosθ-4+3-4cosθ+4/3

=2cosθ+1/3,

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