Question

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
​

Answer 1

Answer:

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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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VIDEO EXPLANATION

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