问题 解答题
a
=(1,2),
b
=(-3,2),k为何值时:
(1)(k
a
+
b
)⊥(
a
-3
b
);
(2)(k
a
+
b
a
-3
b
)?
答案

(1)∵

a
=(1,2),
b
=(-3,2),

且(k

a
+
b
)⊥(
a
-3
b
),

∴(k

a
+
b
)•(
a
-3
b
)=(k-3,2k+2)•(10,-4)

=10(k-3)-4(2k+2)

=10k-30-8k-8

=2k-38

=0,

解得k=19.

(2)∵

a
=(1,2),
b
=(-3,2),

∴k

a
+
b
=(k-3,2k+2),

a
-3
b
)=(10,-4).

∵(k

a
+
b
a
-3
b
),

k-3
10
=
2k+2
-4

解得k=-

1
3

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单项选择题