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已知向量a,b满足1/5(a+3b)-1/2(a-b)=1/5(3a+2b),求证:向量a与b共线,并求a的绝对值:b的绝对值
人气:436 ℃ 时间:2020-09-21 10:22:50
解答
1/5(a+3b)-1/2(a-b)=1/5(3a+2b)
=>a/5+3b/5-a/2+b/2=3a/5+2b/5
=>(1/5-1/2-3/5)a=(2/5-3/5-1/2)b /*把ab移两边*/
=>9a=7b
=>a=7/9 b
=>a与b共线,and |a|:|b|=7:9=7/9
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