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TS EAMCET 20-July-2022 Shift 1 Solved Paper
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© examsnet.com
Question : 32
Total: 160
Let
a
,
b
,
c
be three unit vectors satisfying
|
a
−
b
|
2
+
|
a
−
c
|
2
=
10
. Then Statement (I) :
|
a
+
2
b
|
2
+
|
2
a
+
c
|
2
=
2
.
Statement (II) :
|
2
a
+
3
b
|
2
+
|
3
a
+
2
c
|
2
=
10
.
Which of the above statements is(are) true?
Statement I is true, but Statement II is false
Statement II is true but Statement I is false
Both Statement I and Statement II are true
Both Statement I and Statement II are false
Validate
Solution:
👈: Video Solution
Given,
|
a
|
=
|
b
|
=
|
c
|
=
1
,
|
a
−
b
2
|
+
|
a
−
c
|
2
=
10
|
a
|
2
+
|
b
|
2
−
2
a
⋅
b
+
|
a
2
|
+
|
c
2
|
−
2
a
c
=
10
⇒
1
+
1
−
2
a
⋅
b
+
1
+
1
−
2
a
⋅
c
=
10
⇒
a
⋅
b
+
a
⋅
c
=
−
3
Statement I
|
a
+
2
b
|
2
+
|
2
a
+
c
|
2
=
|
a
|
2
+
4
|
b
|
2
+
4
a
⋅
b
+
4
|
a
|
2
+
|
c
|
2
+
4
a
⋅
c
=
1
+
4
+
4
+
1
+
4
(
a
⋅
b
+
a
⋅
c
)
=
10
+
4
(
−
3
)
=
−
2
≠
2
Statement I is false.
Statement II
|
2
a
+
3
b
|
2
+
|
3
a
+
2
c
|
2
=
4
|
a
|
2
+
9
|
b
|
2
+
12
a
⋅
b
+
9
|
a
|
2
+
4
|
c
|
2
+
12
a
⋅
c
⇒
4
+
9
+
9
+
4
+
12
(
a
⋅
b
+
a
⋅
c
)
=
26
+
12
(
−
3
)
=
−
10
≠
10
© examsnet.com
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