Question

the angle between a vector and b vector is p/ 3 and the angle between two a vector and -3 b vector ​

Answer 1

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┗_________∞◆∞_________┛

Angle between A and B = π/3 = 60°

Here,

A is multiplied by 2  => 2A

B is multiplied with -3 => -3B

Multiplying any vector with a scalar does not change its direction but since B is multiplied with negative sign its direction will be reversed

Hence

Angle between 2A and -3B = 60 + 180

                                               = 240° = 4π/3 radian

Answer 2

Answer:2pi/3

Explanation:

Step 1: Draw vector  

a

 and  

b

    [Ref. Fig.1]

Step 2: Draw  2

a

 and −3

b

          [Ref. Fig.2]

Vector 2

a

 will be twice the length of  

a

 in the same direction.

Vector −3

b

 will be of thrice the size of vector  

b

 but in opposite direction.

Let ϕ be the angle between 2

a

 and −3

b

.

   ϕ=π−

3

π

​

=

3

2π

​

Hence, Angle between 2

a

 and −3

b

 is  

3

2π

​

.