How do i.... Find the angle between each pair of vectors below. (1 point each) a. a = 2x + 3y a = 4x + 2y

Question

asked Dec 25, 2019 160k views

1 Answer

Houman · Answer 1 · 2019-12-30T17:40:26+0000

Recall that the dot product between two vectors
$\mathbf a$ and
$\mathbf b$ satisfies

$\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta$

where
$\|\mathbf x\|$ denotes the norm of a vector
$\mathbf x$ , and
$\theta$ is the angle between the two vectors.

So if
$\mathbf a=(2,3)$ and
$\mathbf b=(4,2)$ , then

$(2,3)\cdot(4,2)=\|(2,3)\|\|(4,2)\|\cos\theta$

$\implies2\cdot4+3\cdot2=√(2^2+3^2)√(4^2+2^2)\cos\theta$

$\implies\cos\theta=(14)/(√(13)√(20))$

$\implies\theta\approx29.7^\circ$