11. If the sum of two unit vectors is also a unit vector,then magnitud

1.	11. If the sum of two unit vectors is also a unit vector,then magnitude of their difference and anglebetween the two given unit vectors is(1) 3,60(2) 3,120°(3) 2,60(4) 2,120°
Answer» CORRECT OPTION is B 3 ,120 ∘ ∣ a + b ∣=1 ∣ a ∣ 2 +∣ b ∣ 2 +2∣ a ∣∣ b ∣cosθ =1 →2(1+cosθ)=1 →cosθ= 2 −1 θ=120 ∘ ∣ a + b ∣= ∣ a ∣+∣ b ∣ 2 −2∣ a ∣∣ b ∣cosθ = 1+1−2cos120 ∘ = 2+2× 2 1 = 3 .

11. If the sum of two unit vectors is also a unit vector,then magnitude of their difference and anglebetween the two given unit vectors is(1) 3,60(2) 3,120°(3) 2,60(4) 2,120°

Answer»

CORRECT OPTION is

B

3 ,120

∘

∣

a

+

b

∣=1

∣

a

∣

2 +∣

b

∣

2 +2∣

a

∣∣

b

∣cosθ

=1

→2(1+cosθ)=1

→cosθ=

2 −1

θ=120

∘

∣

a

+

b

∣=

∣

a

∣+∣

b

∣

2 −2∣

a

∣∣

b

∣cosθ

=

1+1−2cos120

∘

=

2+2×

2

1 =

3 .

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11. If the sum of two unit vectors is also a unit vector,then magnitude of their difference and anglebetween the two given unit vectors is(1) 3,60(2) 3,120°(3) 2,60(4) 2,120°​

CORRECT OPTION is

B

3

,120

∘

∣

a

+

b

∣=1

∣

a

∣

2

+∣

b

∣

2

+2∣

a

∣∣

b

∣cosθ

=1

→2(1+cosθ)=1

→cosθ=

2

−1

θ=120

∘

∣

a

+

b

∣=

∣

a

∣+∣

b

∣

2

−2∣

a

∣∣

b

∣cosθ

=

1+1−2cos120

∘

=

2+2×

2

1

=

3

.

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11. If the sum of two unit vectors is also a unit vector,then magnitude of their difference and anglebetween the two given unit vectors is(1) 3,60(2) 3,120°(3) 2,60(4) 2,120°