Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)

Question

a= <2,2> b=<2,-1>

exact=

approximent=

Answer 1

You can use the equation for a dot product: a·b = |a| |b| cos(θ), where θ is the angle between the vectors a and b.

We can calculate |a| and |b|:

|a| = √(2²+2²)=√8=2√2

and

|b| = √(2²+(-1)²)=√5

We also know that a·b = (a_x*b_x + a_y*b_y)

= 2*2 + 2*(-1)

= 2

We can re-arrange the original equation, and plug in values:

cos(θ) = a·b ⁄ |a| |b|

cos(θ)= (2) ⁄ (2√2 * √5)

cos(θ)= 2 ⁄(2√10)

cos(θ) =1 ⁄ √10

Take the inverse cosine of both sides, giving you the answer:

θ =cos^-1(1 ⁄ √10)

≈ 72°