Question

The |⃗ + ⃗⃗| = |⃗| + |⃗⃗|, then angle

between ⃗ ⃗⃗ will be

a. 90°

b. 120°

c. 0°

d. 60°​

Answer 1

Answer:

The correct answer is Option a. 90°

Explanation:

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Answer 2

a and b are unit vectors and ( 3a − b ) is also unit vector

To find: Angle B/w and b

Suppose angle b/w a and b is θa .

b =∣ a∣∣ b ∣cosθ (Dot product of two vectors)a .

b =cosθ as aand b are unit vector

so ∣ a ∣=∣ b ∣=13

a − b is also unit vector i.e. 3a − b∣=1

( 3 a − b ) 2 =1⇒( 3 ) 2 ∣ a ∣ 2 +∣ b ∣ 2 −2 3 a .

b∣=1

3(1)+(1)−2 3

cosθ=1 as a.

b =cosθ

So, 4−2 3

cosθ=1⇒3=2

3 cosθ

cosθ= 23

✅✅ i.e θ= 62 or 60°✔✔

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