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CBSE Class 12 Math 2008 Solved Paper

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Question : 10
Total: 29
For what value of λ are the vectors
→
a
 = 2
^
i
+λ
^
j
+
^
k
 and
^
b
 =
^
i
−2
^
j
+3
^
k
 perpendicular to each other?
Solution:  
→
a
 = 2
^
i
+λ
^
j
+
^
k
^
b
 =
^
i
−2
^
j
+3
^
k
If
→
a
 and
→
b
 are perpendicular to each other, then
→
a
.
→
b
 must be 0.
→
a
.
→
b
 = 2
^
i
+λ
^
j
+
^
k
 .
^
i
−2
^
j
+3
^
k
0 = 2 - 2λ + 3
2λ - 5 ⇒ λ =
5
2
Thus, the value of λ is
5
2
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