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CBSE Class 12 Math 2008 Solved Paper

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Question : 9
Total: 29
Find the angle between the vectors
→
a
 =
^
i
−
^
j
+
^
k
 and
→
b
 =
^
i
+
^
j
−
^
k
Solution:  
→
a
 =
^
i
−
^
j
+
^
k
→
b
 =
^
i
+
^
j
−
^
k
Now ,
→
a
.
→
b
 = |
→
a
||
→
b
|cosθ
Where θ is the angle between
→
a
 and
→
b
 ; also 0 ≤ θ ≤ π
^
i
−
^
j
+
^
k
 ,
^
i
+
^
j
−
^
k
 = (√12+(−1)2+12) (√12+12+(−1)2) cos θ
⇒ 1 - 1 - 1 = 3 cos θ
- 1 = 3 cos θ
cos θ = −
1
3
 ⇒ θ = cos−1(−
1
3
)
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