shashacoco
幼苗
共回答了17个问题采纳率:88.2% 举报
∵|向量CA|=|向量CB|=3,∠C=90°,∴|向量AB|=3√2,且向量AC·向量BC=0.
∵向量AM=向量MN=向量NB,∴向量AM=(1/3)向量AB、向量BN=-(1/3)向量AB.
∴向量CM·向量CN
=(向量AM-向量AC)·(向量BN-向量BC)
=[(1/3)向量AB-向量AC]·[-(1/3)向量AB-向量BC]
=-(1/9)|向量AB|^2+(1/3)向量AB·向量AC-(1/3)向量AB·向量BC+0
=-(1/9)×(3√2)^2+(1/3)向量AB·(向量AC-向量BC)
=-2+(1/3)向量AB·(向量CB-向量CA)
=-2+(1/3)向量AB·向量AB
=-2+(1/3)|向量AB|^2
=-2+(1/3)×(3√2)^2
=-2+6
=4.
1年前
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