Question

Given vectors u = ⟨2, –3⟩ and v = ⟨1, –1⟩, what is the measure of the angle between the vectors?

Answer 1

The Answer is A. 11.3

Explanation:

got it right. Also thats just the letter answer :)

Answer 2

The measure of the angle between the vectors = Ф = 11.30°

Explanation:

Given

• u = ⟨2, –3⟩

• v = ⟨1, –1⟩

`\mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}`

Next, find the lengths of the vectors:

`\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrtx_i\right`

u = ⟨2, –3⟩

`\:\:\left|u\right|\:=√(2^2+\left(-3\right)^2)`

`=√(13)`

u = ⟨2, –3⟩

`|v|=√(1^2+\left(-1\right)^2)`

`=√(2)`

Finally, the angle is given by:

`\mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}`

cos (Ф) = 5/√26

Ф = arc cos (cos (Ф)) = arc cos (5 √26) / (26)

Ф = 11.30°

Thus, the measure of the angle between the vectors = Ф = 11.30°