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CBSE Class 12 Math 2012 Solved Paper

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Question : 11
Total: 29
If
→
a
,
→
b
,
→
c
 are three vectors such that |
→
a
| = 5 , |
→
b
| = 12 and |
→
c
| = 13 and
→
a
+
→
b
+
→
c
 = 0. Find the value of
→
a
.
→
b
 +
→
b
.
→
c
 +
→
c
.
→
a
Solution:  
Considering dot product on both sides,
(
→
a
+
→
b
+
→
c
) . (
→
a
+
→
b
+
→
c
) = 0 . 0
⇒ |
→
a
|2+|
→
b
|2+|
→
c
|2 + 2 (
→
a
.
→
b
 +
→
b
.
→
c
 +
→
c
.
→
a
) = 0
⇒ 52+122+132 + 2 (
→
a
.
→
b
 +
→
b
.
→
c
 +
→
c
.
→
a
) = 0 = 0
⇒ 2 (
→
a
.
→
b
 +
→
b
.
→
c
 +
→
c
.
→
a
) = - 388
⇒ (
→
a
.
→
b
 +
→
b
.
→
c
 +
→
c
.
→
a
) = -
338
2
 = - 169
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