Given v=3i and w= 9i+2j ​, find the angle between v and w.

Answer 1

The easiest way to find the angle between two vectors is to follow this formula.

cos(Θ) = (v • w)/(|v| * |w|)

v • w is the dot product n this case

3i • (9i + 2j) = 3*9 + 0*2 notice there is a hidden 0j in v

v • w = 27

|v| is the magnitude of v (it uses the same symbol as absolute value) This is the length of the vector.

The magnitude formula is √(v₁² + v₂²)

|v| = √(3² + 0²) = √(3²) = 3

|w| = √(9² + 2²) = √(85)

So now the angle is

cos(Θ) = 27/(3*√(85)) = 0.97618

Using trigonometry

Θ = acos(0.97618) = 12.53º

This is the angle between the vectors.