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Q.

If angle between a→ and b→ is π3, then angle between 2a→ and −3b→ is

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a

π3

b

2π3

c

π6

d

5π3

answer is B.

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Detailed Solution

Step 1: Draw vector a and b    [Ref. Fig.1] Step 2: Draw  2a and −3b          [Ref. Fig.2]Vector 2a will be twice the length of a in the same direction.Vector −3b will be of thrice the size of vector b but in opposite direction. Let ϕ be the angle between 2a and −3b.    ∅=π-π/3=2π/3 Hence, Angle between 2a and −3b is 2π/3​.  2π3
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If angle between a→ and b→ is π3, then angle between 2a→ and −3b→ is