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CBSE Class 12 Math 2013 Solved Paper

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Question : 8
Total: 29
a unit vector
→
a
 makes angle
π
3
 with
^
i
,
π
4
 with
^
j
 and acute angle θ with
^
k
 , then find the value of θ.
Solution:  
Let
→
a
 = x
^
i
+y
^
j
+z
^
k
 be the unit vector.
∴ x = cos
π
3
 =
1
2
y = cos
π
4
 =
1
√2
Now, x2+y2+z2 = 1
⇒ (
1
2
)2+(
1
√2
)2+z2 = 1
⇒ z2 = 1 -
1
4
−
1
2
 =
1
4
⇒ z =
1
2
∴ cos θ =
1
2
 ⇒ θ =
π
3
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