Two vectors have magnitude 2 m and 3 m. The angle between them is 60°. Find a) the scalar product of two vector. b) magnitude of their vector product.

Ans: Consider two vectors a and b.

Given : | 𝑎 | = 2m and 

| 𝑏 | = 3m 

Angle between vector a and vector b is 60°, say θ = 60°

(a) Scalar product:

a.b = |a| |b| cos θ

= 2 x 3 x cos 60°

= 6 x 1/2

= 3 m²

(b) magnitude of vector product:

|a x b| = |a| |b| sin θ

= 2 x 3 x sin 60°

= 6 x √3/2

= 3√3 m²