CBSE Class 12 Math 2018 Solved Paper

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Question : 3
Total: 29
Find the magnitude of each of two vectors
a
and
b
, having the same magnitude such that the angle between them is 60 and their scalar product is
9
2
Solution:  
Given that the magnitude of each of the two vectors
a
and
b
have same magnitude.
|
a
|
= |
b
|
... (i)
the angle between
a
and
b
is 60°
⇒ θ = 60°
and
a
.
b
=
3
2
... (iii)
Since,
a
.
b
= |
a
|
|
b
|
cos θ
|
a
|
|
a
|
cos 60° =
9
2
From (i),(ii) and (iii)
|
a
|
2
×
1
2
=
9
2

|
a
|
2
= 9
|
a
|
= 3
|
a
|
= |
b
|
= 3 ... From (i)
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