.(1)设向量a,b满足|a|=|b|=1及|3a-2b|=7,求|3a+b|的值.(2)在数列{an}中,已知a1=1,1an+1=1an+12,(n∈N+),求a50..-数学

题目简介

.(1)设向量a,b满足|a|=|b|=1及|3a-2b|=7,求|3a+b|的值.(2)在数列{an}中,已知a1=1,1an+1=1an+12,(n∈N+),求a50..-数学

题目详情

.(1)设向量
a
b
满足|
a
|=|
b
|=1及|3
a
-2
b
|=
7
,求|3
a
+
b
|的值.
(2)在数列{an}中,已知a1=1,
1
an+1
=
1
an
+
1
2
,(n∈N+),求a50..
题型:解答题难度:中档来源:不详

答案

(1)由题意可得 9
a
2
-12
a
•b
+4
b
2
=9-12
a
•b
+4=7,∴
a
•b
=class="stub"1
2

|3
a
+
b
|=
(3
a
+
b
)
2
=
9
a
2
+6 
a
b
+
b
2
=
13

(2)∵a1=1,class="stub"1
an+1
=class="stub"1
an
+class="stub"1
2
,∴{class="stub"1
an
}是以1为首项,以class="stub"1
2
为公差的等差数列,
class="stub"1
an
=1+(n-1)class="stub"1
2
=class="stub"n+1
2
,∴an=class="stub"2
n+1
,∴a50 =class="stub"2
51

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