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CBSE Class 12 Math 2013 Solved Paper

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Question : 20 of 29
Marks: +1, -0
If
→
a
 and
→
b
 are two vectors such that |
→
a
+
→
b
| = |
→
a
|, then prove that vector 2
→
a
+
→
b
 is perpendicular to vector
→
b
Solution:  
|
→
a
+
→
b
| = |
→
a
|
⇒ |
→
a
+
→
b
|2 = |
→
a
|2
⇒ |
→
a
|2 + 2
→
a
.
→
b
 + |
→
b
|2 = |
→
a
|2
⇒ 2
→
a
.
→
b
 + |
→
b
|2 = 0 ... (1)
Now, 2
→
a
.
→
b
 .
→
b
 = 2
→
a
.
→
b
 +
→
b
.
→
b
 = 2
→
a
.
→
b
 + |
→
b
|2 = 0
We know that if the dot product of two vectors is zero, then either of the two vectors is zero or the vectors are perpendicular to each other.
Thus,2
→
a
+
→
b
 is perpendicular to
→
b
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