Question

determine vector a ×vector b given vector a=2i +4j and vector b = 3j +5j ​

Answer 1

Given

a= 2i+3j+4j

b=3i+4j+5k

The scalar product of these two vectors is-

a.b= |a| |b| cosθ

Where θ is the angle between the two vectors.

(2i+3j+4j)(3i+4j+5k) =

|a| |b| cosθ

Or,

6+12+20 = |a| |b| cosθ

Where,

|a| =sqrt(2^2+3^2+4^2)

|b|= sqrt(3^2+4^2+5^2)

Therefore,

38= sqrt(29).sqrt(50)cosθ

cosθ= 38/sqrt(1450)

cosθ=38/38.07

cosθ= 0.998

θ= 1.54 degree.

The angle between the two vectors will be about 1.54 degree.