If the sum of two unit vectors is also a vector of unit magnitude, the magnitude of the difference of two unit vectors is
A) 1 unit
B) 2 units
C) root 3 units
D) Zero
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Explanation:
MATHS
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is
October 15, 2019avatar
Arman Rathiya
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ANSWER
Let
a
,
b
be two unit vectors whose sum is also a unit vector
c
a
+
b
=
c
...... (i) and ∣
a
∣=∣
b
∣=∣
c
∣=1
Now, magnitude of sum of
a
and
b
is
∣
a
+
b
∣=∣
a
∣
2
+∣
b
∣
2
+2(
a
⋅
b
)
⟹1=1+1+2(
a
⋅
b
) ..... From (i)
⟹
a
⋅
b
=−
2
1
Magnitude of their difference is given by
∣
a
−
b
∣
2
=∣
a
∣
2
+∣
b
∣
2
−2
a
.
b
=1+1+2×
2
1
=3
⟹∣a−b∣=
3
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