问题 解答题
已知
a
=(1,1),
b
=(x,1),
n
=
a
+2
b
,v=2
a
-
b

(1)若
n
=3
v
,求x;
(2)若
n
v
,并说明此时两向量方向相同还是相反.
答案

a
=(1,1),
b
=(x,1),

n
=
a
+2
b
=(1,1)+(2x,2)=(2x+1,3),

v
=2
a
-
b
=(2,2)-(x,1)=(2-x,1).

(1)∵

n
=3
v

∴(2x+1,3)=3(2-x,1),

解得x=1.

(2)∵

n
v

∴2x+1=3 (2-x),∴x=1.

此时,

n
=(3,3),
v
=(1,1),

n
=3
v

∴n与v方向相同.

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