2018˸߿½ѵ3

ѵ3

ƽ½̲ĸĸӵ֮һȫʹ½̲ĵĸ߿𽥼Ӵ˶ⲿݵĿȣҪǰһЩ.

ѵų

()ABCУA(5-1)B(-17)C(12)(1)BCϵ

AMij;(2)CABƽADij;(3)cosABCֵ.

̽

[1]ͼ֪ƽABCDA1B1C1D1ĵ檩ABCDΣҡC1CB=C1CD=BCD.

(1)֤C1CBD.

(2) ֵΪʱʹA1CƽC1BD?֤.

ͼҪ鿼ӦֱнǵԼ弸ͼεĽ.

֪ʶУ֤弸еĴֱ⣬ʹʹ֤ü.

ѵǿĿеλùϵϵ໥תپҪ֪ṩĽнǵϵ.

뷽ab a·b=0ֱ֤ߴֱֻҪֱ֤߶ӦΪ㼴.

(1)֤ =a, =b, =c,⣬|a|=|b| ɼнΪȣ =a-b =c(a-b)=c·a-c·b=|c|·|a|cos-|c|·|b|cos=0,C1CBD.

(2)⣺ʹA1CƽC1BDֻ֤A1CBDA1CDC1

=(a+b+c)·(a-c)=|a|2+a·b-b·c-|c|2=|a|2-|c|2+|b|·|a|cos-|b|·|c|·cos=0,

|a|=|c|ʱA1CDC1֤ͬ|a|=|c|ʱA1CBD

=1ʱA1CƽC1BD.

[2]ͼֱABCA1B1C1ABCУCA=CB=1BCA=90°AA1=2MNֱA1B1A1Aе.

(1) ij;

(2)cos< >ֵ;

(3)֤A1BC1M.

ͼҪ鿼еķ弸.

ＶĿ.

֪ʶУǽǡĿռֱϵO-xyz,ҵ.

ѵǽϵ󣬿ȷҵ.

뷽ҵxOyڵABC꣬Ȼģҳĵ.

(1)⣺ͼCΪԭ㽨ռֱϵO-xyz.

ãB(010)N(101)

| |= .

(2)⣺ãA1(102)C(000)B1(012).

= =(012)

=1×0+(-1)×1+2×2=3

| |= (3)֤ãC1(002)M( )

A1BC1M.

1.ʱһҪƽơϳɡֽȱ任ȷؽĸ㣬ıʵʶ.λתнϵ˼.

2.йȣֱӰнǵ.ֱ֤Ĵֱƽ;ļнǹʽ;빫ʽռֱߵļнǺ.

3.ÿռ弸һɰ¹̽˼

(1)Ҫʲô֪ʶ?ҪõЩ?

(2)ҪǷ֪?δ֪Ƿ֪תɵֱӱʾ?

(3)Ҫֱ֪תɵʾǷֱĸδ֪ʾ?Щδ֪֪תкιϵ?

(4)Ѿʾ㣬ܵõҪĽ?

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