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

If angle between $\vec{a} a n d \vec{b} i s \frac{π}{3},$ then angle between $2 \vec{a} a n d - 3 \vec{b}$ is

A
$\frac{π}{3}$
B
$\frac{2 π}{3}$
C
$\frac{π}{6}$
D
$\frac{5 π}{3}$

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.

$\emptyset = π - π / 3 = 2 π / 3$

Hence, Angle between 2a and −3b is $2 π / 3$ .

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