Find the vector of length 2 that makes an angle of π/4 with the positive x axis
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Answer:
Correct option is
C
−
2
i
−
2
j
+
2
k
Let
a
^
=li+mj+nk where l
2
+m
2
+n
2
=1
a makes an angle
4
π
with z-axis
∴n=
2
1
⇒l
2
+m
2
=
2
1
....(i)
then,
a
^
=li+mj+
2
k
Now,
a
^
+i+j=(l+1)i+(m+1)j+
2
k
...(ii)
Its magnitude is 1, hence
(l+1)
2
+(m+1)
2
=
2
1
...(ii)
From Eqs (i) and (ii) we get
2(l+m+1)=0
⇒(l+m)
2
=(−1)
2
l
2
+m
2
+2lm=1
⇒2lm=
2
1
⇒l=m=−
2
1
Hence,
a
^
=−
2
i
−
2
j
+
2
k
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